A DETERMINATION OF THE
MICROSTRUCTURE OF COPDLYMERS

Thesis for the Degree of Ph. D.
MICHIGAN STATE UNIVERSITY
THEODORE M. FISCHER, JR.
1968

MI ICHIGAN

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This is to certify that the
thesis entitled
A DETERMINATION OF THE
MICROSTRUCTURE 0F COPOLYMERS

presented by

THEODORE M. FISCHER, JR.

has been accepted towards fulfillment
of the requirements for

Mdeqree inw CHEMISTRY

     

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Date DECEMBER 6. 1968

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ABSTRACT

° A DETERMINATION OF THE MICROSTRUCTURE OF cepcmmas

by Theodore M. Fischer Jr.

A series of vinylidene chloride (VClz)-isobuty1ene (IB) copolymers
and vinylidene chloride-vinyl chloride (VCl) copolymers were polymerized
to low conversions. The copolymers were dissolved in bromobenzene and
an NMR spectrum run of the solutions. From these spectra, sequences of
diads and tetrads were determined for the VClz-IB copolymers and died
sequences were determined for the VClz-VCl copolymers.

The experimental measurements of the diad sequences in the VClz-IB
copolymer system were used to determine the reactivity ratios for the
monemers in this system assuming a terminal kinetic mechanism of copoly-
merization. This represents a new technique for determining reactivity
ratios which is independent of chemical or spectrographic analysis of
the mole fractions of the mere. The values of these reactivity ratios
were used to calculate theoretical tetrads but the results correlated
poorly with the experimental tetrads. Sufficient experimental detail
was available to determine the four parameters of the penultimate
kinetic mechanism.of copolymerization. Good correlation for the mole
fractions of the monomers, diads and tetrads were found using the
experimentally determined values r1=2.95, r1'=6.22, r2=0.15, and r2'=0.02
from the penultimate mechanism.

In the VCIZAVCl copolymer system the experimental measurements of

the diad sequences were used to obtain the monomer reactivity ratios

Theodore M. Fischer Jr.

based on the terminal mechanism.of copolymerization. Good agreement was
obtained between calculated and experimental values for the diads with
the values for r1=3.75 and r2=0.18. However, the possibility of
another copolymerization mechanism could not be ruled out because as
Berger and Kuntz pointed out longer sequences are needed for a critical
analysis and only diad sequences could be measured in this copolymer
system.

Two series of VClZ-IB copolymers were made at various conversions
up to 50% to investigate the dependence of diad sequences on conversion.
A theoretical treatment has been developed for the terminal mechanism of
copolymerization and the trends predicted between average diads and
conversion by this theory using the values r1=3.30 and r2=0.05 correspond

to the experimentally predicted curves.

A DETERMINATION OF'THE'HICROSTRUCTURE'OF'COPOEIMERS

By

4 V
\ ‘P\ {11‘

v

Theodore M." Fischer Jr.

A THESIS

Submitted to
Michigan state University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of chemistry

1968

ACKNOWLEDGMENTS

I wish to express my sincere appreciation to Dr. Jack B. Kinsinger
for his patience and assistance during the course of this investigation.
I also wish to acknowledge Dr. C. W. Wilson, III whose assistance was
invaluable in this investigation.

I would like to thank Michigan State University for the financial
aid and teaching experience gained from my teaching assistantship.

Lastly I want to express my gratitude to my wife for her many
sacrifices and assistance in preparing this manuscript and for her

urgings without which this work could not have been completed.

.ii

TABLE OF CONTENTS
Page

EMICAL MODUCTION O O O O O O O O O O O O O O O O O O O O 1
mm 0 O O O O O O O O O O O O O O O O O O C O O O O O O O 0 1h
mm-AL C O O O O O O O ‘ O O _ O O O O O O O O O O O O O O O 3 2

Purification of Monomers and Initiator. . . . . . . . . 32
Preparation of Low conversion chz-IB Cepolymers. . . . 33
Preparation of Low Conversion VClé-VCI copolymers . . . 36
Heparation of High conversion Copolymers . . . . . . . 36
Preparation of Copolymers for NHR Analysis. . . . . . . 39

ImmmATIONOOOOOOOOOOoo’eeeoeoooeoee ’41

Methods of Obtaining 111MB Spectra. . . . . . . . . . . . hl
Methods of Measuring Areas Underneath Peaks.. . . . . . I43

WATIONOFNIRSPETRA......._.......... I414
Assignments of Peaks in vclg-IB Copolymer Spectra . . . hit

Peak Assignments in Virvlidene chloride-le Chloride
CopolymerSpectra....’............. S2
Normalization of the MIR Spectra. . . . . . . . . . . . S6

ammrsmnrscussrou.................... 60

Results of VOlz-IB Copolyner System . . . . . . . . . . 60
Results for vc12-VC1'cop01ymer System . . . . . . . . . 81;
Results of conversion Study . . . . . . . . . . . . . . 92
canal-union.eoeeeeeeeeeeeeeeeeoeee 96

BMW 0 . O O O O O O O O O O O O O O O O O O 0 O O O O 99
mm C O O O O O O O O O O O O O O O O O O O O O O O O O O 102

iii

‘LIST OF'TABLES

Table Page
I. Peak assignmentinn methoxy proton region by Harwood
”d Ritchey. O O O O O O .0 '0 O O O O O O O O O O O 10
II. ‘Peak assignments in methamy proton region by Ito and
ImahitaC O O O O O C C 0 ~ 0 O O O O O O O O O O O 12
III. ‘Equations for monomer and sequence fractions. . . . . 2h
IV. Instantaneous diad fractions. .1. . . . . . . . . . . 30
V. Average mole fraction after conversion. . . . . . . . 31

VI. CopolymerizatiOn of vinylidene chloride and
“abutyleneoeeeeeeee’eeeeeeeeeee 35

VII. Copolymerization of vinylidene chloride and vinyl
Chloride O O O C O O O O O O O O O O O . O O O O O O 37

VIII. High conversion copolymerization runs of vinylidene
chloride and isobutylene . . . . . . . . . . . . . ho

IX. Hole fractions of diads . . . . . . . . . . . . . . . 62

x. copolymerization reactivity ratios fron‘data'for'

vinylidene chloride (l)-isobutylene (2) system . . 63
XI. mole fractions of tetrads . . . . . . . . . . . . . . 69
III. ‘Vinylidene chloride-vinyl chloride copolymerization . 85
XIII. Cupolymerization reactivity ratios from various data
for vinylidene chloride (1) «1:31 chloride (2)
mt” O O O O O O O O O O O O O O O O O 0.. O O O 86
XIV. ‘Vinylidene chloride-isobutylene copolymer conversion
serieseeeeeeeeeeeeeeeeeeeeee 92

iv

LIST OF FIGURES

Figure Page

1. A typical plot of the probabilities of the stereosequences
versus 0' for styrene-methyl methacrylate copolymer. . . . 5

2.1 Hethylnethacrylate centered triad Configurations of Ito
and Imhita: O O O O O O O O O O O O O O O O O O O O O O 12

3. Praton resonance spectra of a honopolymer of isobutylene (A);
a homopolymer of virvlidene chloride (D); a copolymer
with mole fraction 0.h8 isobutylene and 0.51 vinylidene
chloride (13); a copolymer with mole fraction 0.2h iso-
butylene and 0.76 vinylidene chloride (0). . . . . . . . . 145

II. Possible tetrad sequences for a VClz-IB copolymer . . . . . . . h?
5. Possible IB centered triads in a VClz-IB copolymer. . . . . . . SO

6. Praton resonance spectra of a copolymer with mole fraction 0.39
isobutylene and 0.61 vinylidene chloride (A); a copolymer
with mole fraction 0.33 isobutylene and 0.67 virglidene
chloride (B); a copolymer with mole fraction 0.21; iso-
butylene and 0.76 vinylidene chloride (0). . . . . . . . . 51

7. Proton resonance spectra of a copolymer with mole fraction 0.17
vinyl chloride and 0.83 vinylidene chloride (A); a co-
polymer with mole fraction 0.26 vinyl chloride and 0.714
vinylidene chloride (B); a copolymer with mole fraction
0.37 vinyl chloride and 0.63 vinylidene chloride (0) . . '. 53

8. Proton resonance spectra of a homopolymer of vim'l chloride
(PVC); a copolymer with mole fraction 0.51 virvl chloride
and 0.I49 vinylidene chloride (D); a copolymer with mole
fraction 0.66 viml chloride and 0.31; vimlidene chloride

(E) 5h

9. Linear plot of the relationship 2Fo= F02( l-fM)r1/fM-r2
where 1'“: mole fraction ofudiads. . . . . . . . . . . 6h

10. Linear plot of the relationship 2Fo( l'erBVZfAB = F0211 + r2
where 1A3 = mole fraction of AB diads. . . . . . . . . . .. 65

11. Linear plot of the Ross-Finemanrelationship, Fo( f-l)=r1F02/f1
where Pa = mole ratio of monomers in the feed and f = mole
ratio of monomer in the copolymer: (0) represent NHR
data; (A) represent carbon analysis data on an x axis
Shift“ for Clarity. O O O O O O O O O O O O O 0 O O O O O 66

V

LIST or mourns (Cont.)

Figure ‘ ’_ 4 f ~ I. _
12. Experimental data from chlorine analysis of the copolymer .
13. ‘Hole fraction of diads versus mole fraction of vinylidene
chloride in monomer feed; (0) f“; (D) 2fAfB';
(A)fBBeeeeeeeeee‘eeeeeeeeeeeee
1h. iHole fraction of tetrads versus mole fraction of vinylidene
chloride in monomer mix: (A) fm; ([3) HM;
(0)1.Bm‘eeeeeeeeeeeeeeeeeeeeee
16. ‘Ratio of IAAAB/fBAAB versus F6. . . . . . . . . . . . ... .
17o Rat1°°ffMBA/fmvar8u8Foeeeeeeeeeeeeeee
18. A linear plot of (fin/TAABAfllrbZ versus Pb . . . . . . . .
19. Same coordinates as Fig. 13; (DMM; (O) 2fm3.(A) fBB .
21. Same coordinates 38 114.; (O) ZfAABA; (D) ZfABAB e e e e e
22. 'Linear plot of the relationship Fb(l-fA1)fAA =:r2/Fo-r1
where fgg== mole fraction of AA diads. . . . . . . . .
23. Linear plot of the relationship 2Fo( l-2fAB)2fm == F0211 + r2
where 1A3 =mole fraction of AB diads. . . . . . . . .
21;. Linear plot of the Ross-Fineman relationship. . . . . . . .
25. Linear plot of theJRosséFineman relationship: ([3) and
dotted line are from carbon analysis, (C)) and
continuous line are from chlorine analysis.. . . . . .
26. ‘Hole fractions of diads of‘VCldV012 system versus mole
fraction of vinylidene chloride in mono-er mix: ((3)
f“; (D)2fAB;(A)fBBeeeeeeeeeeoeeee
27. Plot ef'mole fraction cf vinylidene chloride in‘VClz-IB
copolyner versus per cent conversion . . . . . . . . .
28. ‘Plot of mole fraction of diads in vclzéIB copolymer system

versus per cent conversion . . . . . . . . . . . . . .

vi

Page

67
70

72
73
77
16
79

81
82

87
88
89
90
93
9h

95

HISTORICAL INTRODUCTION

Before 1959 the only Nuclear‘Magnetic Resonance (NMR) studies
of polymers undertaken were limited to broadline studies of solid
polymers. The first paper on high resolution NMR was published by
Bovey, Tiers, and Filipovich (1) who investigated the NMR spectrum
of a carbon tetrachloride solution of polystyrene. The local field
effects were overcome by dissolving the polymer in a suitable liquid
to separate the nuclei and Bovey and Tiers hoped to obtain a narrow
peak spectrum similar to the spectra of organic liquids. The spectrum
they obtained was broader than normally found for ordinary organic
liquids, but still much narrower and with greater detail than found in
the broadline spectra of solid or molten polymers.

The polystyrene solution spectrum consisted of two main peaks
with the larger one downfield split into two poorly resolved peaks at
3.1T and 3.5T where 7' equals

A(MehSi)~106
10 .-

 

Oscillator frequency (cps.)

and [I is the line separation between sample and reference in cycles
per second (cps.) (2). The peak further upfield was at 8.h7'. The
doublet downfield was attributed to resonances of the protons on the
phenyl group, and the peak upfield was assigned to the methylene
protons of the polymer chain. A third peak was expected for the
CX-nydrogens but was not located.

To investigate the cause of the splitting of the proton resonances
of the phenyl group Bovey, Tiers, and co-workers ran spectra of some

1

2
substituted polystyrenes (poly-2-chlorostyrene, polyeB-chlorostyrene,
and poly-h-chlorostyrene). The smaller peak was not found in the
poly-2-chlorostyrene but was detected in both the others. From this
it was concluded that the smaller peak was due to the resonance of
the ortho hydrogens of the phenyl group.

Bovey, Tiers, and co-workers identified the expected (X—lrydrogen
peak by running an NHR spectrum.of poly:£},£3—d2~8tyrene. This polymer
had no methylene protons, but a peak was present in the region where
the methylene proton resonance was found in the polystyrene spectrum.
They concluded that the CXEhydrogens resonated further upfield than
expected from the spectra of small molecule analogs.

Bovey, Tiers, and co-workers noted that the width of the larger
phenyl peak was about 20 cps. wide compared to about 5 cps. for the
phenyl peak in cumene which is a small molecule analog of polystyrene.
Thus it was established that although some of the finer details could
not be seen in high resolution NHR of polymers as in ordinary organic
liquids, much information could be obtained from these data.

Bovey, Tiers, and co-workers observed that the line width of the
spectrum was independent of the molecular weight of the polystyrene at
least down to a molecular weight of 10,000. NHR spectra of several
different high molecular weight species of polystyrene were run but
the line width remained constant. The line width was shown also to be
independent of the concentration of the polymer provided it was less
than 50-60% wt./vol. Bovey and Tiers concluded that the peak widths
were essentially independent of macroscopic viscosity and were a measure

of local viscosity in the immediate vicinity of each chain segment.

3

Bovey, Tiers, and co-workers noticed that the spectrum of poly-
styrene with less than 10 units lost the ortho phenyl peak and the
larger peak shifted to correspond to the one for cumene at 2.8h7’. The
Clyhydrogen resonance peak was observed inthis short chain polystyrene.
They also took NHR spectra of some polystyrene samples of different
tacticities but obtained identical spectra for all of them.. From this
data.Bovey, Tiers, and co-workers concluded that due to steric re-
strictions polystyrene of more than 10 units existed in a quasi-
crystalline state in solution which placed the ortho hydrogens of one
phenyl ring more in the diamagnetic region of its neighboring phenyl
rings than the meta or para hydrogens.

Kern and Pustinger (3) in another early investigation of polyb
styrene observed partially resolved CX-hydrogen and methylene proton
peaks for isotactic polystyrene, whereas, an HER spectrum of a commercial
atactic polystyrene sample showed only one peak for these protons.

The NMR study of tacticity or stereosequences has been the main
subject of NHR investigations in the field of polymer microstructure.

A second paper by Bovey and Tiers (h) dealt with the, MR study of the
poly(methylmethacrylate)(PMHA). The NHR spectra of two differently
prepared PUMA samples were run in the solvent, chloroform. One sample
was synthesized with a free radical initiator which gave a random
distribution of stereosequences, whereas the other was synthesized with
an anionic catalyst and led predominately to an isotactic polymer.

Bovey and Tiers designated three different stereosequences in the chain,
an isotactic sequence, "1", a heterotactic sequence, Ph", and a syndic-
tactic sequence, Is". Each of these sequences contains three monomer

units as pictured below.

 

 

 

 

 

I “H3 I I3 I IH3
—c—I:L c s C—c*— m
I I: I I I
H mCH3 H COOCH3 H COOCH3
III CH3 H COWHB H COOCH3
(II—II I II I I "h"
H COOCHB H CH3 A CH3
I I3 I Im3 I CH3
_I—II——I’_I* I I
H COOCH3 H CH3 H COOCH3

‘where 6* represents an asymmetric carbon.

In the PMMA polymer spectra the proton resonances of the (XEmethyl
group consisted of three peakS. These peaks were assigned to the three
different stereosequences. The per cent of each stereosequence in the
polymer is proportional to the area under each peak.

Bovey and Tiers designated a parameter,(f , as the probability
that a polymer chain would add a monomer unit to give the same configura-
tion as the last unit of the chain. This assumes that (T'is independent
of the penultimate unit. Thus propagation could be described by a
single value of (f and the probabilities of the three stereosequences

were described as follows:

P1 = 0’2 w (1.1)
Pa: (1 --o’)2 (1.2)
Pr." 1 ' 1’1 - Pa: 2(6-0’3 ‘ (1.3)

For free radical polymerizations this relationship was shown to hold

within experimental error, but it was in poor agreement for stereopolymers

5
formed by ionic polymerization. A typical plot of the above relations

is depicted in Figure 1.

1.0

 

0.8

0.2

(a
(>53

1’! A
0. // . . I .

0.0 0.2 Ooh 0.6 008 1.0
f

Fig. l. A typical plot of the probabilities of the stereosequences versus
(f for styrene-methyl methacrylate copolymer. (CD isotactic;
(CDheterotactic; LAO syndiotactic. Solid lines represent theoretical
values.
Another important contribution made by Bovqy and co-workers

 

 

 

appeared in a paper in 1963 (S), where he and co-workers reported

studies on several polymer systems, among them was poly(vinyl chloride). I
They used H—fi spin decoupling to aid in the determination of the
structure and configuration of the polymer. They were able to discern
that the complex methylene proton region consisted of two overlapping
triplets which originated from the racemic and meso methylene configura-
tions. The decoupled CXEproton resonance area consisted of three peaks
corresponding to the three different possible stereosequences. The

undecoupled.CX-hydrogen spectrum was more complex and was interpreted

6
to consist of three overlapping quintets which would have been difficult
to resolve without the aid of the H-H spin decoupling.

miller and co-workers (6) studied the configuration of poly-
(methacrylic anhydride). They prepared several samples of the polymer
by different polymerization methods and obtained an NHR spectrum of
each. They found disagreement with the simple P vs. 6 relations
"( 1.1), (1.2), and (1.3) of Bovey and Tiers. They interpreted this poor
agreement to the. assumption that 0' was independent of the penultimate
effect and explained their results by invoking a penultimate mechanism
for their system.

Brownsteinand co-workers (7) investigated a series of poly-
CX-aethyl styrenes. They prepared polymers by cationic, anionic, and
free radical initiation and found the fraction of each stereosequence
in the polymers from the areas under the three different peaks of the
proton resonances of the O(-methyl group. They constructed a P vs.6
graph and obtained a reasonable fit with experimental results.

In the last two or three years considerable work has been undertaken
in high resolution NHR of polymers. This work has been concentrated
for the most part in two main areas: stereosequential studies of
homopolymers and sequence distribution studies of copolymers.

The stereosequential studies of homopolymers have been reported
on a number of polymers including poly-( propylene)(8?-10), poly( styrene)
(11, 12), poly( (X—methylstyrene)(7, 13), poly(vinyl chloride)(5, 13-19),
poly(vinyl fluoride)(5, 20), poly( trifluorochloroethylene)(21) ,
poly( vinyl methyl ether)(5, 22, 23), poly( a-methylvimrl mettwl ether)
(2h), poly( vinyl acetate)(5, 25), poly( vinyl trifluoroacetate)(25),
P01y( vinyl alcohol)(25) , poly( isopropyl acrylate)(26), poly( metlvlacrylate)

7 .

(27, 28), poly(methyl,methacrylate)(h, 29-33),:poly(acetaldehyde)(34), and
poly(acrylonitrile)(62,63). Considerable information on homopolymer
structure has now been obtained from these studies. One important outcome
has been the detection of sequence lengths of four monomeric units inNMR spectra.

Compared to the tacticity studies of homopolymers few studies of
sequence distributions in copolymers have been undertaken. .Bovey reported
the first proton NMR study of a copolymer (35). He studied the copolymer
of methylmethacrylate and styrene by varying the monomer ratios in a
series of copolymerizations. Unfortunately the spectra of these samples
were rather complicated and while an attempt was made to interpret the
spectra, Bovey admitted that his results were rather inconclusive and
that additional work was needed in this area.

The best resolution in copolymers was reported by Ferguson who in
1960 (36) studied the copolymers of vinylidene fluorids-hexafluoropropylene
utilizing F19 NMR. These copolymers were prepared by persulfate initiated
emulsion polymerization. Ferguson deduced the fraction of different
types of repeating units in the chain of which four were possible according
to his analysis. The units were designated as:

CFB
( -CH2 ”CFZ'CFZ-CF) 9
623

(CH2-CF2-CF-CF2) ,

(CHQ'CFZ‘CHZ'CFZ) 9
and (-CH2-CFQ'CF2'CH2)
which he called U, V, W, and X respectively. No hexafluoropropylene-
hexafluoropropylene repeat units were found to be present. Ferguson defined

a quantity "n" as the fraction of vinylidene fluoride units in w and X

8
and analyzed the gross structure from NMR as:
(“0.93Vo.o7)1-n(“o.9510.05)n/2 ,
which showed that a slight amount of head-head and tailitail polymerization
took place. .

‘Wilson in 1962 (37) published a short note on F19 NHR study of a
copolymer of tetrafluoroethylene and hexafluoropropylene. The bulk
copolymer sample was heated to 310° C before a narrow band spectrum was
obtained. The spectrum consisted of three peaks, one.peak due to the
F19 resonance of a CF3 group, a peak due to the F19 resonance of a CF?
group, and a peak due to the F19 resonance of a CF group. ‘Wilson reported
a determination for only one sample called Teflon-100 and stated that
the mole % of hexafluoropropylene was 9.0% t 1.5%.

CbuJo and co-workers in l96h (38) reported a proton NHR study of
the vinyl chloride-vinylidene chloride copolymerization system. In this
paper they proposed that some of the vinylidene chloride units polymerized
in head-head sequences although there is no evidence of head-head
polymerization in the homopolymer of vinylidene chloride. They based
their interpretation on the NMR study of a series of copolymers prepared
from different monomer feed ratios plus the NHR of polyvinylidene chloride,
poly-2,3-dichlorobutadiene and partially chlorinated,polyh2,3-dichloro-
butadiene. Their interpretation of their spectra is questionable as no
full spectra were shown in the publication and only a partial spectrum
of one copolymer was displayed. An alternate interpretation which may
explain their results is contained in this work.

Recently two notes pertaining to the NMR study of the copolymeriza-
tion of styrene and methyl methacrylate have been published (39, hO).

iBoth papers base their analysis on the proton resonance peaks of the

9

methoxy groups which are two atoms removed from the backbone of the
chain. The note by Harwood and‘Ritchey (39) attempts to correlate the
interpretation of the data with Bovey's three previous assumptions (35)
that: (a) only adjoining monomer units affect the resonance of the
methoxy protons; (b) the distribution of a given type of triad of monomer
units among isotactic, syndiotactic, or heterotactic configurations was
constant throughout the copolymers; and (c) the resonance of methoxy
protons centered in a triad of three methylmethacrylate (EMA) units
occurred entirely in the lowest field methoxy peak, irrespective of the
triad configuration just as in PUMA. From assumption (a) the three
methoxy resonance areas should be related to the distribution of INA
centered triads in the copolymers.

The methoxy resonance occurred in three peaks at 6.507', 7.057’,
and 7.h57r. .According to Ritchey and Harwood if Bovey's assumptions
were valid the percentage of methoxy resonance (P) which occurred in
each peak should be related by equation (l.h) to the percentage distribu-
tion of the‘HHA centered triads (x‘HHM, Z sun, and % SHS) in a copolymer
and should also be related to the respective fractions (X, Y, Z) of
triad resonances which occurred in each peak.

P=onsus+rzsrm+zazmm (1.10

From assumption (c) Z should equal unity for the lowest field
methoxy resonance (6.507') and zero for the other two resonances. The
following rearranged equations were then obtained from equation (1.h)
and used in a simple test of the validity of Bovey's assumptions.

(P650 ' z m) :1: + Y-

Zsms zsns (1.5)

$314M

 

10

PMS z x. + p. 1. 3""
5 SMS ' 4 z SMS (1'0)
Pms :11. + y... % SW (1.7)

 

1 SMS 1% SMS

A plot of the left hand side of the equations (1.5, 1.6, and 1.7)
vs. (z sun / z SMS) should give straight lines with slopes Y, Y', and
I" respectively and intercepts of X, X', and 1" respectively. Harwood
and Ritchey's data show the predicted straight line behavior when the
spectra were obtained with the polymer dissolved in carbon tetrachloride,
however, for the copolymers dissolved in o-dichlorobenzene the lines had
definite curvature to them. Harwood and Ritchey'proposed that the
o-dichlorobenzene spectra could be correlated with calculated EMA data
centered pentad distributions. Their calculations showed good agreement
between experimental and calculated values if they used monomer reactivity
ratios of 0.52 and 0.h6 for the copolymerization parameters for styrene
and MHA respectively. They assigned six of the ten possible MHA centered
pentads to specific methoxy resonance peaks. These assignments are in
Table I.
Table I. Peak assignments in methoxy proton region by

Harwood and.Ritchey

 

 

 

Peak A, 6.57' Peak B, 7.057' Peak 0, 7.hS7'

MMH MSMMM MSMSM

SMHSM SSMMM $(ssnss)
[Semen] ssums

4 ssuss) %[SSMSM3

fi<ssuss)

11

Because of stereochemical effects Harwood and Ritchey believe some
of the pentads show in all three peaks. However, no absolute experimental
proof on small molecule models or deuterated species was offered for
these assignments.

The same copolymer system was studied by Ito and‘Iamashita (hO),
but they proposed a different interpretation. They concluded the three
peaks in the methoxy resonance region were spectroscopically distinguish—
able as three kinds of’HMA units. They assigned the various possible
HHA centered triads to these peaks and included the configurations of
the triads in their assignment. The various triads and their configura-
tions are depicted in Figure 2 where the units above.the horizontal bar
are in the d configuration relative to the central‘H unit and those below
the bar in the 1 configuration. The assignments of the various peaks
are listed in Table II. For simplicity the peak designations are the
same as those of Harwood and.Ritchey. This interpretation does not
extend to the pentads but it is not in conflict with the triad assignments
proposed by Harwood and Ritchey. Ito and yamsshita introduced a parameter,
C7, which they defined as the probability of alternating H and S units
taking the same configuration (dd or 11). From the theory of copolymer-
ization they calculated the triad mole fractions from literature values
of the monomer reactivity ratios. Using these calculated values they
then calculated a value for C7 of 0.h8:t 0.0h. From this value of
Cfthey calculated the areas under the three peaks of the methoxy protons
and compared them with the measured areas. They claimed good agreement
was obtained.

Ito and‘Iamashita (hl) also studied the Run spectra of several

styrene-methyl acrylate copolymers obtained by free radical intitiation

12

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

M M M )1 M ‘ M M M
MMM: (a)I I I0») I I(c)l I I(<1)I I |
M ”M M I M
ms, [M I I I ’I I I rI I I I I
s M M s

(e) (f) (g) In)

em: I’ "I ’I ’I I I I I
l I F I
s M s M M

M s s M

ans. (1)? ’1 aka) I I(k)l I (1) I ,
I A 1
S s

Fig. 2 methylmethacrylate centered triad configurations of Ito and

Yamashita

 

Table II. Peak assignments in methoxy proton region by Ito and

 

 

 

Yamashita
Peak A PBak B Peak C
1*
a,b,c,d, e,g, i
f,h,l j,k

*Letters refer to configurations of Figure 2

 

13
and used the same type of analysis as they conducted in the styrene—
methylmethacrylate systems. The resolution of the peaks was poor and
the results were not as good. They obtained ad = 0.80 for this system.

Two earlier reports by Kato and coaworkers (42, 43) on the NMR
spectra of sytrene—methyl methacrylate copolymers have been reported,
but because of poor resolution only relative amounts of styrene and
methyl methacrylate in the copolymers were determined and monomer
reactivity ratios were computed. These values compared favorably with
previous literature values.

iMuch more recent work subsequent to this work in this area with
the better instrumentation now available has been done on copolymers of
methyl methacrylate and methyacrylate (64) and copolymers of vinylidene
chloride with vinyl acetate (65, 66, 67), methyl methacrylate (66),
°(-methy1 styrene and styrene (66). A comprehensive review of the NMR
studies of elastomers in solution was just published this year (68).

The NMR spectra of copolymer systems studied to date have been
complicated by the asymmetric centers in the copolymers. The interpre-
tation of the NMR spectra of these copolymers has been very difficult
because of the various stereosequential configurations possible for each
copolymer sequence.

In this study two copolymer systems were studied. The first system
was the vinylidene chloride-isobutylene system which consists of two
symmetrical monomers whose favorable geometry eliminated all complications
due to asymmetric centers and much of the poor resolution in spectra ob-
served by earlier workers. The second system studied was vinylidene
chloride-vinyl chloride which can be interpreted despite the presence of

an unsymmetrical monomer.

THEORY

In free radical copolymerization as in ordinary free radical
homopolymerization the simple mechanistic chain reactions which lead to
the formation of a polymer molecule consists of three steps; initiation,
propagation, and termination. The chemical composition of high
molecular weight copolymers is dependent in first approximation only
on the propagation step of the chain reaction.

If one of the monomers in a copolymer is designated A and the
other B it can be shown that if the addition of these monomers to the
growing radical were dependent on the makeup of the entire polymer
radical then an infinite number of different reaction rates would occur
since the process would be chain length and composition dependent. It
was postulated as early as 1936 by Dostal (uh) that,the kinetic behavior
of the chain radical was dependent only on the terminal group (the
monomer unit last added to the growing chain) and the kinetic behavior
was independent of the length or over-all composition of the polymer
chain.

Under these conditions the composition of the copolymer chain is

determined by the following four propagation reactions:

~A° + A—'~AA' (2.1)
~A-+ B--~AB- (2.2)
~B-+ B-—~BB- (2.3)
~B-+ A-’~BA° (2.1:)

whose forward rates are written as:

1:11 [Ac] [A] , (2.5)
lb

.15
k12 [11-] [B] (2.6)
k22 [B] [B] (2-7)
1:21 [3-] [A] (2.8)
Dostal was able to write correct mathematical expressions for the
rate of capolymerization and the composition of a copolymer in terms of
these rates, but since fourunknown rate constants were designated he
could not devise any experimental tests for his conclusions.
‘wall in l9hl (hS) showed that the chemical composition of copolymers
was dependent only on relative reactivities of the two monomers to the
two radicals.. He expressed these relative reactivities in the form of

ratios called "monomer reactivity ratios" and defined them as:

k11 k22
r1 ._.._ __ and r2 -_- _
k12 k21

Mayo and Lewis (h6) in a classic work, undertook a eystematic
study of copolymerization and arrived at the following rate expressions

for the consumption of monomers A and B:

193%] = k11 [11°] [111+ k21 [3’] [A] (2.09)
5-1-3?) = k12 [A5] [B] “(22 EB'JEBJ (2-10)

In the steady state of copolymerization the different types of free
radicals must be maintained at a steady concentration, therefore,

1:12 [11-] [B] = k21 [13:] [A]. This means that in the steady state the rate

at which (A-) is destroyed is equal to the rate at which (B') is destroyed.
It is then possible to solve for the concentration of one of the radicals
in the steady state in terms of the other. 'Mayo and Lewis applied this

steady state assumption to the ratio of the disappearance of the two

l6

monomers and arrived at the following relation:

(5.1.) m + [B]
* (2.11)

 

which using the definition of monomer reactivity ratios defined by*wall
can be simplified to:

LL53... In ”103+”?
am 3] r2[B'_]+[A] (2°12)

It follows that the ratio of the rates of disappearance of the
two monomers is also the ratio of the molar concentrations of the two
monomers in the copolymer. Defining the instantaneous concentration of
monomer A in the copolymer as "a" and the concentration of monomer B

in the copolymer as ”b" then;

a _ (In) r1 [A] +[BZI
'- '- '- (2.13)
b B] r2 [BIN [A]

This equation is known as the "copolymer composition equation". This

 

same equation was derived independently by Alfrey and Goldfinger (h?)
at approximately the same time using the same reasoning.

The copolymer composition equation has been used primarily for
the evaluation of the monomer reactivity ratios, r1 and.r2. The experi-
mental technique has been developed into a standard routine and consists
of preparing a series of the copolymers for a given A and B by varying
the monomer concentrations and analyzing the resulting» copolymers for
the concentration of “a" and "b". The conversion of the copolymerizations
in this series must be kept low because equation (2.13) is valid for

instantaneous copolymerization and the assumption is made that low

17
conversion copolymerization approximates instantaneous copolymerization.
The most common method of determining r1 and r2 from this data is the
method of Fineman and Ross (h8). It consists of rearranging the copolymer

composition equation to the linear form;

mr-nfi'= qflfi.r2 ”J”

a. J » .2 *
where F=B and f—b. A plot of F(f - 1) vs. Fz/f will result in a
"'7F"‘-

straight line with a slope of r1 and an intercept on the F(f - 1) axis
of ~r2. This method gives the most accurate results because the data
can be plotted and a least squares method or a nonlinear least square
can be applied to determine the slope and intercept. Since the derivation
of the copolymer composition equation, its use has been extended to
include other aspects of copolymer composition. most recently it has
been used to calculate various monomer sequences in copolymer chains.

‘Merz and co-workers (h9) derived a copolymer composition equation
in l9h6 which included the effect of the penultimate unit on the addition
of a monomer in a growing chain. The derivation is similar to the
derivation of the simple copolymer composition equation for the terminal
effect, however, eight propagation reactions and four monomer reactivity

ratios or twofadditional parameters are needed to define the propagation

steps. The monomer reactivity ratios were defined as

1‘1 = klll
k112
r1! = k211

k212

18

k
k221
k
r2 ' z 122
k121

where the subscripts describe the propagation reaction according to

monomeric units. The copolymer composition equation was:

1+(flf)
(rzB) (r2'B + A)
1+ — ——-—
A rlB 1— A

Equation (2.15) reduces to (2.13) by setting r1' = r1 and r2I= r2.

rl'B +A

 

 

EIIE?
em

Since copolymerization is a discrete statistical process, Herz
and co-workers (h9) also found it convenient to describe the copolymeri-
zation process in terms of four conditional‘Markov probabilities. One
can define a general Markov conditional probability P13 as the probability
that monomer "3" adds to a polymer chain whose terminal unit is "i".
For a copolymerization system four permutationsof this probability

exist, P11, P12, P21, and P22. These probabilities are defined as

 

 

follows:
P11 _ 1:111! - rlA
k11A 4- k12B _ 1‘11I 1* B (2'16)
1: B
k211i A

 

k21A + kzzB A + r2B

l9

k-B rB
22: 22 2

 

 

(2.19)
k21A + k22B A+ r2B ’

‘Hith these definitions the distribution of various sequence lengths of

A and B in the copolymer chain can be calculated in the following manner.
A sequence is defined as any run of A's or S's. The probability that a
sequence starting with an.A is followed by an A is'P11 according to the
principle of succeeding probabilities. If the sequence then contains

nA units the probability for this run would be P11(n'1). Since the

run is terminated by a.B unit the probability of termination is P12 or

(1'Pll)' Thus the probability that an A sequence picked at random
contains Just nA members is:

N( a,n1) = P11I n1-1)(1—211) (2.20)

This is called the "number distribution function" for the lengths of
A sequences and was first derived by Herz and Alfrey.

Here recently Price (50) utilized a matrix method to realize
the copolymerization process in terms of’Harkov chain theory. He
applied the matrix scheme to the three simplest examples of copolymer-
ization: the terminal unit effect (considering the active end to
be Just the last monomer unit added), the penultimate unit effect
(considering the last two monomer units as the active end), and the
penpenultimate unit effect (active and consisting of the last three

monomer units).

20

Price preferred binary notation for a polymer chain. By
labeling one monomer "0* and the other monomer ”l" he designated
any chain sequence by the decimal equivalent of the binary number,
e.g. a chain segment 1001 would be 9 in the decimal system. I

A Markov process is defined by two probabilities: the a,
prioriprobability, 123(k), and the conditional probability, P”.
The a priori‘PJ(k) is the fraction of unit sequences of length k.
Thus the letter "k" signifies the number of units which affect the
addition of a monomer unit. The letter *3" is the decimal equivalent
of the binary notation described by the sequence, e.g.‘P2(2) is the
probability that a given pair is 10. Pr; is the conditional
probability that a given state "r" is followed by a state “a! where
"r" and "s" are expressed as decimal notations of the binary sequences.

Thus any sequence may be described by an initial probability
of finding the first one, two, three, etc. units multiplied by the
conditional probabilities of converting the initial sequence to
various other sequences, e.g. for the case of the terminal effect the
sequence 011001 may be described by‘Pb(1)P01P11PldedP01, for a pen-
ultimate unit effect the same sequence would be described by
21(2)1>13r32?20901. The conditional probabilities 2,, are subject to
the restriction 2:2b3'2 1 since a given terminal sequence must add a
0 or a l, and sighs a given singlet, diad, triad, etc. must be in some
state 2130‘): 1.

Sdnce the conditional probabilities which are more often called
transitional probabilities depend only'on the initial and final state

resulting from the addition of a single unit to the end of a chain and

21
do not depend on the state of the chain at any prior time they then fit
the definition of a Markov chain.

To solve for the copolymer composition for any specific (k) the
transitional probabilities are arranged in a matrix (P) the elements of
which are Prs where r is the column and is is the row.* The steady-state
distribution of singlets if k=l, diads if k = 2, etc. in states 0 to
2k-l is given by solutions of the equation (P)V(k)= A V(k) where
V(k) is a 2k element column vector whose components represent the
relative concentrations of the various states and is a constant. Because

of the restriction that 2 Prs = l, the matrix (P) is stochastic. Using

5
the fact that the matrix is stochastic the various components, Vj(k), can

be found (see Appendix I for detailed solution). If No is defined as
the number of 0's in the completed chain and N1 as the number of 1's

in the completed chain then an equation for N0 can be derived from

N
1
this matrix. According to Price it is:

2(h;-2)
2
No: 0 e
(k-l) (2.21)
gvd
1

where 'e' is an even integer and 'd' is an odd integer. An expression
for 59. in terms of the various probabilities is obtained by substituting

N1

the appropriate probabilities into the Vj(k) expressions. It should be

N
DOtGd that fi9..is Price's nomenclature for the expression a in equation
1
(2.21).

Price defined kro and krl as the specific rate constants for

addition of monomers 0 and 1 respectively to the growing chains ending

*Price's preference here is unfortunately not the usual nomenclature
used in Markov chain matrix theory in that r is generally given as
the row and s the column.

22

in terminal sequence "r" and he defined Mo and M1 as the.monomer feed
concentrations of O and 1 respectively; These notations differ from
previous work,therefore the table below is given to aid in translating

Price's work into the more familiar terminology.

NOMENCLATURE
Price Mayo
’19. 2.
N1 b
M0, 141 A, B
r0, r1 r1, r2
(terminal ( terminal
mechanism) mechanism)
r0, r2, r3, r1 r1, rl', r2, r2'
(penultimate (penultimate
mechanism) mechanism)

The rate constants used by most workers contain two subscripts for the
terminal mechanism, three for the penultimate mechanism and so forth in

contrast to only two subscripts in Price's rate constants regardless of

- k
the mechanism under consideration. He further defined rn:= E22 when
n1
"n" is even and Efll when In" is odd and further sets
kno
Prs 2 E3 (2.22)

krth
where u==0 when "s" is even and u:= 1 when "s" is odd. By substituting

this expression for the transitional probabilities into the equation for

N_0 and letting 3.9, = F0 Price obtains copolymer composition equations in

N

1
terms of Fb and ”the reactivity ratios rn for the three different copolymer-

23
ization mechanisms (See Appendix.I for a specific example). The express-
sions derived by this method for the penultimate and terminal mechanisms
are the same as those derived by earlier workers, showing that Price
has not proposed any new mechanism but only a new mathematical tool
for arriving at these more complex expressions.

Price also derived general formulas for the fraction of monomer 0
in the copolymer, the fraction of 01 monomer sequences in the copolymer,
and the fraction of sequences containing only monomer "0! or monomer "1"
for a given length n. These equations are given in Table III.

In addition to these, equations can be obtained from.this method
for the fraction of sequences of any length from any "active and sequence"
in terms of the parameters, the monomer reactivity ratios, and initial
monomer concentrations, provided the conversion is kept low.

In the past decade a number of copolymer systems have appeared to
have compositions whose values do not correlate well with the terminal
mechanism for copolymerization. Previous to high resolution NHR studies,
however, all compositional data had been based only on the mar fractions
in copolymer chains. The accuracy of these data are.highly variable
depending on the particular method of analysis and justification for
invoking the penultimate mechanism.as an explanation for these discrepancies
is subject to considerable question. This was first shown by Berger and
Kuntz (51) in l96h whose analysis of reasonably high precision compositional
data taking into account the drift in monomer feed over the conversion
range could not justify distinguishing between the terminal and penultimate
mechanisms. They further concluded that additional information on the
sequence lengths or copolymer microstructure would be needed to make this

distinction.

21:

Table III. Equations for monomer and sequence fractions

 

 

K-l

 

 

7” (k)
k
N N
0+ 1 :viuc)
=0

1: = 1 r01 = f0(1)P01

3
k : 2 :01 = v1(2)/ Eon”)

k = 3 £01 = (v2(3)+V3(3))/§7:v1(3)

iao

pnm: henna-k)

Where n = number of 0's or 1's in the sequence

X‘= O or 1

K‘l
Px(k) = Vx( k)/ ZZV1(k)

i=0

 

25

To further complicate the nomenclature problem Harwood and
Ritchey‘(52) introduced a new parameter,'R, called the run number and
defined it as the average number of monomer sequences occurring in the
copolymer per 100 monomer units. They used this parameter and the
ratio of the monomer concentration to derive an equation similar to that
of the Ross-Fineman equation except for the insertion of the parameter R.

A problem.which has only recently'received attention is the
determination of copolymerization reactivity ratios at higher conversions;
that is, drift in monomer feed ratios. The theoretical treatments which
have been discussed previously are all valid only for instantaneous
copolymerization which allows F to be treated as a constant, F0. As
long as the copolymerization proceeds to no more than a few percent in
conversion these treatments can be assumed to be valid, however, if the
reaction is allowed to proceed to any great extent these equations will
no longer apply. They are not valid because as the process continues
one of the monomers will enter into the copolymer chain more rapidly
than the other unless the monomer reactivity ratios are equal and this
will change the ratio of the monomer feed. The theoretical treatments
discussed previously are all dependent on the ratio of the monomer con-
centration thus the results based on these treatments will change with
the degree of conversion.

A general formula for obtaining the copolymer composition for

any conversion was developed by Skiest (53) and is shown below:

M _ 1
1" is ‘[ F141" “1 (2.23)

26

where M=Ml + M and MO=M10+ M20. For given values of the reactivity

2
ratios, graphical or numerical methods can be used to calculate the
expected change in the monomer mixture and copolymer composition corres-
ponding to the mole conversion, 1 - g .

For an ordinary binary copolymgrization assuming only terminal
unit effects Meyer and Lowry (5%) have recently developed an analytical

solution to Skiest's equation. Meyer and Lowry noted the equation for

the mole fraction of monomer M1 in the feed.

F1 = (r1 - 1)f12 + fl (2.2a)

 

(Pl + P2 - 2) £12 + 2(l-P2) £1 + P2

could be substituted into Skiest's equation and rearranged to obtain:

A +1
in y. = 1 (Dr? r2-2) f12 + 2(1-1‘2) f1 '0' r2 ‘ (2.25)
O (2-1'1-1'27 dfl
f (fl-l) (fl - l - P2 )
p0

 

 

2 - rl-r2
In this form the equation can be expanded and integrated where the final

integrated equation is:

: £1 a f2 ’8 flo - 6 Y
o —— (2.2s)
flo f2° f1 ‘ 5

:3“:

 

 

where a = r2
8 = r1
7 = 1 ‘rir‘z

 

(l - r1)(l - r2)

27

(5:: l - r2
(2 - r1 - r2)
with the condition r1: 1 and r2 9‘. l.
Kinsinger (55) used different nomenclature and solved the problem
in a different manner and obtained the same relationship. Since the

present work uses the nomenclature of Kinsinger, his definitions are

listed below:

P11] and P14 : monomer concentrations in the feed at am total conversion.
@110] and [r120 2 initial monomer concentrations.

0:1 = conversion of monomer l.

O( 2 -.: conversion of monomer 2.

__ (-1! _ _(H1+M2)
CX—l "0‘1

 

 

 

(2.27)
M (H10 + H20)
1 -o(=f1°(1 -O(1) + r2°(1 -O(2) (2.28)
f1°._. ["10] ; . r2°___ [”24 (2.29)
["1°]+ [“2”] [”1°]+["2°]
r<a>=££=f1°‘1 "0(1) zru" 0‘1) (we)

 

 

0
f2 f2°(1 ~09) (1 - 0(2)

The differential equation expressing the momentary ratio of the disappear-
ance of the two monomers is shown below using the nomenclature of

Kinsinger and is identical to (2.12) on page 16.

(1041) _ F0 d(l - 0(1) F (rlF-+— l)

__ _ : __ (2.31)
d(H2) d(1 - 0(2) (r2 4-F)

 

28
By substitution of equation (2.30) with (2.31) and elimination of
d(1 -O(1) and (1 -O(1) the equation can be integrated in the limits

from 1 to (1 - (X2). The completed integration is:

 

 

ln(1-O(2)= 1'2 1n 2‘ + 1 " 1'1’"2 ‘ 1n[(’1'1)F+(1'r2) (2.32)
1-r2 F0 (rl-l)(1-r2) L(r1-1)Fo+( l-r2)

It is possible to rearrange (2.28) so that:

(1 ~00 = (1 -O@)r2° [F+ 1] (2.33)
and substituting into (2.32) one obtains:

 

 

1n(1-O()=lnf2°+ln[F+1] + —r_2_ ln_F_' +
(1 - 1‘2) Fe
1 .. rlrz 1n (r1-1)F+(l-r2) J (2.31.)
(r1-1)( l-r2) (r1-1)Fo+ (l-r2)

An equation similar to equation (2.32) can be derived from
equation (2.30) by applying equation (2. 29) and eliminating d(l -O(2)

and (l - a2). Using the same procedure one obtains:

 

 

 

ln(l-O()=ln [Ej+ 1 1“ F__+
F 1'4'2 F0
1 .. :er lnl:(r1-1)F+(l-r2) ] (2.35)
(r1-1)(1-r2> (r1-1)F.+(1-r2) J

By combining (2.314) and (2.35) and rearranging them one obtains:

a b
(1'00 =[(r1-1)F+(1-r2) J + f10[:] + £20 [E- ]c (2.36)

 

( r1-1)Fo+( l-rg) F0 F2

where a Z 1 - 1'11‘2
(r1 - 1)(1-r2)

 

29

b = l
l " r2
c = r'2
1 - r2
If the substitutions = and l - a = __ are made and the
—— ._ M , .
o F o
f2f1 0

equation rearranged one obtains the expression of Meyer and Lowry.

Kinsinger has also developed a set of equations for obtaining
the average value of the mole fraction of the various sequences at any
conversion ( a ). He obtained this set of equations by integrating the
equations for the various instantaneous diads between the limits of Po
and P, where Po is the ratio of the initial monomer concentrations and
F is the ratio of the monomer concentrations after any conversion. The
instantaneous diad fractions and their integrated forms are displayed
in Tables IV and V. 2

Before the present work no experimental work was published on

the mole fraction of diads or higher sequences as a function of conversion.

30

Table IV. Instantaneous diad fractions

 

 

 

 

2
r'F
l o
1r,“L :
rlFo2 4“ 2Fo+ r2
2F
2f'AB :_ o
1'117'02'4” 2Fo + 1'2
r
fBB : 2

 

 

31

Table V. Average diad mole fraction after conversion

 

 

 

 

 

 

 

 

 

 

 

 

 

F 2
-f— _ PlFo
AA ' dF
rlF°2 + 2F°+ r2
0
- 1 ln R1 + 2 - r1r2 in R2
r1 2r1 / l-rlr2
= + l for rlrz < l
P - F0
F
23:- _ 2202
AB - dF
rlFo + 2?0 + r2
Po
1 ln R1 - 1 1n R2
r
- 2r y’I - r r
' l l 1 2 fer r1r2 < %
F — P
o
F
._ r
= 2
fBB dF
rlFO2 + 2Fo 1» r2
F
0 1‘2 1nR2
= 2 u/ l - rlrz
P - F0

2
F + 2F + r2

Where R1 - r1

 

and R2 rlf + l - ./I - r1r2-1 . rlFo + l + #1 - rlr2.]
riP + l + H? r1r2 rlf‘o + l - .1]. - rlr2 J

 

 

 

EXPERIMENTIL
Purification of’Monomers and Initiator

1. Azo-bis-isobutyronitrile (AIBN) - The AIBN obtained from
Monomer-Polymer Laboratories was purified by recrystallization from
acetone. A large quantity was dissolved in warm acetone until a saturated
solution was obtained. The solution was filtered through a.Buchner
funnel under vacuum and transferred to a beaker. The beaker was cooled
in an ice-water bath for thirtyminutes and a copious crop of crystals
precipitated. The contents of the beaker were again filtered through a
Buchner funnel under vacuum and the residue placed in a vacuum oven to
dry at room temperature.

After drying, the purified, crystalline AIBN was stored in two
twelve dram vials in a refrigerator until needed.

2. Vinylidene chloride (V012) - The V012 was purchased from
Monomer-Polymer Laboratories. The container was stored in a refrigerator
with only the approximate amount needed for each run withdrawn at one
time. The sample withdrawn was separated from dissolved inhibitors by
pouring it through a column of activated alumina (Sb),then it was
transferred directly into the polymerization tubes.

3. Isobutylene (IB) - A two pound cylinder of IE was obtained
from Matheson co.,Inc. (To free the monomer of moisture, it was passed
through a column of drierite then into a condenser surrounded by a dry
ice-acetone bath. The 18 was liquified directly into the vessel in

which it would be used.

0

32

33
h. 'Vinyl chloride (VCl) - The vCl was obtained in a gas qylinder

from'Hatheson Co.,Inc. To purify the monomer of H01 it was bubbled
through a hog aqueous potassium hydroxide solution,then passed through

a column of drierite and soda lime,then passed into a condenser surrounded
by a dry ice-acetone bath and liquified directly into the vessel in

which it would be used.
Preparation of Low Conversion‘VClz-IB Copolymers

Heavy walled combustion tubes (15 x 20 x 250 mm.) were used for
the copolymerizations. The tubes were modified by narrowing the necks
and sealing a 2h/h0 female joint to the top. The initiator (AIBN) was
weighed separately and then charged to the tube. The amount of AIBN
used never exceeded 1% by weight of the total charge. The tube containing
the initiator was closed with a ground glass stopper then weighed on a
Mettler balance. Next the solvent, tetranydrofuran, (THE) was added
and weighed. This liquid was found to be a convenient solvent for the
reaction since the copolymer was insoluble in the monomer mixtures. The
amount of THF added varied according to the amount of V012 since greater
portions of solvent were needed to effect a homogeneous,polymerization
for the greater concentrations of'VClg. The amount of solvent never
exceeded one third of the total weight of the mixture. Next the purified
V012 was added and the tube was reweighed. The amount of‘VClz varied
from one charge to another as a series of copolymerizations with varying
monomer concentrations were planned. After weighing the V612 charge
the tube was placed in a dry ice-acetone bath and the IB condensed
directly into it. ‘When sufficient IB had been added, the tube was connected

with a unit consisting of a vacuum stopcock and a male ball joint. The

3n
tube with the stopcock in the closed position was then transferred to a
Dewar flask containing liquid nitrogen. After the contents had solidified
the tube was attached to a vacuum line via the ball joint and degassed
for three minutes. At the end of this time the tube was sealed off at
the narrowed neck. After cooling, both parts of the tube were weighed
to obtain the weight of the IB by difference.

The sealed tube was placed in a 30° C water bath. After the
contents reached bath temperature the tube was taken from the bath,
shaken and replaced into the bath where it was irradiated with U.V.
light from a Hanovia S-H lamp. The proper polymerization time for low
conversion was judged by eye and depended upon the nature of the charge.
The samples which contained large portions of IE polymerized slowly while
those with large amounts of VC12 needed a much shorter time. Table VI
shows the relative amounts of each monomer in the charge, the weight
percentage of AIBN, the length of the polymerization, and the conversion
for the series. All runs were kept to low conversion.

Polymerization was stopped by removing the tube from the water
bath and freezing it with liquid nitrogen. After the contents were
solidified the tube was broken and the contents after warming were poured
through a coarse sinter glass filter into methanol where the copolymer
precipitated. The polymer was allowed to settle until the supernatant
was clear then the solution was decanted and more methanol was added.
This solution was allowed to stand for 24 hours then decanted from the
solids. The copolymer was then placed in a vacuum oven at 40° C and
dried until constant weight was achieved. The length of time necessary
to attain constant weight varied according to the nature of the copolymer.

The greater the amount of IE in the copolymer the longer it took for a

35

Table VI Copolymerization of vinylidene chloride and isobutylene

 

 

 

Mole Mole Polymer-

FTac- Frac- Wt % ization % con-
Sample tion tion AIBN time in version

V012 IB minutes
v1-32-2 0. 5814 0.h16 1.0 150 h.0
VI-2h-2 0.505 0.105 0.85 100 7.h
v1-12-1 0.1.71 0.529 0.78 250 1.1
VI-22-2 0.h18 0.582 0.75 250 6.0
VI-28-2 0.391 0.609 0.80 300 6.2
v1.30-2 0.353 0.6117 0.88 330 5.5
VI-20-l 0.318 0.682 0.82 1:20 h.5
v1-23-1 0.317 0.683 0.71; 300 2.6
VI—26-2 0.288 0.712 0.83 390 5.6
v1-17—2 0.2147 0.753 1.67 570 9.1;
VI—20-2 0.225 0.775 0.9h 1:80 6.1
v1-25-1 0.213 0.787 0.77 h20 2.0
v1-25-2 0.206 0.791: 0.811 h20 3.8
VI-26-1 0. 198 0. 802 0. 80 1.20 2 .2
VI—18-2 0.159 0.8111 1.25 660 7.3
VI-l6-2 0. 130 0. 870 0. 92 1200 8. 8
vI-29-1 0. 126 0. 87h 0. 87 690 2.14
VI-Bh-l 0. 121 0. 879 0. 93 750 2 . 8
VI-l9-2 0.083 0.917 1.00 720 3.3

 

36
constant weight to be reached. The drying time varied from 2 days to

as much as 10 days.
Preparation of Low Conversion‘VClgéVCl COpOlymers

Since the boiling point of V61 is approximately that of ID the
same preparative technique was used for this system as described in the
previous system. The time needed for these copolymerizations was con-
siderably shorter, but the technique was the same in all other respects.
As with the VClz-IB system enough THF was used in each polymerization
to keep a homogeneous solution and no precipitation of the polymer from
the solution occurred. Table VII shows the mole fraction of each
monomer in the charge, the weight percentage of AIBN, the length of the

polymerization, and the conversion.
Preparation of High conversion Copolymers

To study the effect of conversion on sequence distribution a
series of‘VClz-IB copolymers were made with the same initial monomer
concentrations but with a range of conversions.

The approximate amounts of catalyst, THF,‘VClz,and IB needed
for the series of conversions to be made were calculated on the basis of
approximately 20 grams of solution for each.polymerization tube.

A single neck, 500 ml. round bottom flask was equipped with a
stopcock, ball Joint, and tube from the stopcock running to the bottom
of the flask. ‘Enough AIBN for the series was weighed separately and
charged to the flask.

The flask was weighed after the AIBN was added, then the approximate

amount of THF was measured volumetrically and added to the flask. Next

37

Table VII Copolymerization of vinylidene chloride and vinyl chloride

 

 

 

Hole Mole Polymer-

Frac- Frac- Ht 3% ization % Con-
Sample tion tion AIBN time in version

V012 V01 minutes
vv01-63-2 0.691 0.309 1.0h 30 0.67
vv01-62-2 0.576 0.h2h 1.32 120 h.13
vvc1-36-2 0.h70 0.530 0.97 120 3.55
vv01-67-2 0.395 0.605 1.00 180 b.6b
vvc1-6h-2 0.355 0.6t5 1.15 180 6.23
vv01-61-2 0.272 0.728 0.6h 120 3.33
vvc1—69-2 0.2h0 0.760 1.03 180 h.h7
WCl-66-2 0.203 0.797 1.21 180 . 11.09
vv01-65-2 0.169 0.831 0.78 195 3.82
vvc1-t7—2 0.098 0.912 0.63 150 b.98
vvc1-70-2 0.066 0.93h 1.06 180 0.h0

 

38
the'V012 was measured and added to the flask, and the flask was again
weighed. - _ .

The flask was then placed in a.Dewar filled with acetone and dry
ice was added until the temperature was approximately -20° c. It was
found that cooling the flask to the normal dry ice-acetone bath temper-
ature of -68° 0 caused the AIBN to precipitate from the solution.

After cooling to -2o° c the m which had been condensed into a
separate oylinder was added to the flask. The flask and contents were
then quickly removed from the cold bath, weighed, and returned to the
bath.

A tared polymerization tube, equipped with a stopcock and ball
joint was placed in a dry ice-acetone bath and attached to the vacuum
line. The tube remained under vacuum for 20 seconds then the stopcock
was closed and the tube was connected at its ball joint to the ball
joint of the round bottom flask. The stopcock of the round bottom flask
was opened,then the stopcock of the polymerization tube was opened
slowly and a portion of the solution was transferred to the.polymeriza-
tion tube. ‘Hhen enough of the solution was transferred both stopcocks
were closed and the ball joints were disconnected. The polymerization
tube was then placed in a.Dewar filled with liquid nitrogen, degassed,
and sealed. Both parts of the tube were retained and the top part
weighed immediately.

This procedure was repeated until all of the charge was transferred
from the round bottom flask. All sealed tubes were stored in a large
Dewar at liquid nitrogen temperature until ready for polymerization.

The tubes were removed from the liquid nitrogen when ready for polymeri-

zation and placed in the 30° 0 bath. After warming to bath temperature

39

they were removed, shaken, weighed, and returned to the bath then sub-
,jected to U.V. light. All copolymerizations took place with no preci-
pitation of the polymer from the charge solution. Two series were run
and Table VIII lists the initial conditions, the length of time of
each run, and the conversion for that run.

The copolymers from these polymerizations were precipitated and
dried the same as has been previously described for the low conversion

cepolymerizations°

Preparation of Copolymers for NMR Analysis

Approximately 0.2 g. of the dried copolymer was weighed into a
1 ml. volumetric flask. The flask was then filled to the mark with the
solvent which in most cases was bromobenzene. One sample was also
prepared in tetrachloroethylene and the same procedure was used. To
aid polymer dissolution the volumetric flask was warmed in hot water
until the copolymer passed into solution. The solution was then trans-
ferred to 0.5 mm. wall NMR tubes. The solution was allowed to cool and
three or four drops of the reference standard, tetramethylsilane (TMS),
were added to the tube.

If spectra of the samples were to.be taken at elevated temperatures,
the tubes were placed in liquid nitrogen and attached to a vacuum line.
The solution in the tube was degassed for two minutes, removed from the
Dewar, and allowed to warm to room temperature. The tube was then
returned to the Dewar of liquid nitrogen and subjected to a vacuum for
another two minutes. This procedure was repeated one more time except the
tube was not removed from the Dewar after the third degassing but was

sealed.

140
Table VIII High conversion copolymerization runs of vinylidene

chloride and isobutylene

 

 

 

Polymer-

ization ‘ 5:
Sample time in Conversion

hours

Run {VI-1:94
wt. Ill—“33.111 gme wt. v01.2=57.21 gms wt. THF=50.h3 ems
wt. AIBN=1.0606 gms Fo=0.9h0
VI-h9-2-7 11.0 11.6.
71449-241 15.3 17.0
VI-h9-2-2 30.0 28.1;
VI-h9-2-5 118.0 36.2
7119-2-8 168.0 h6.3
VI-h9-2-6 72.0 117.7
VI-h9-2-3 106.0 52.7
Run #VI-l-B

wt. 13:29.50 gas wt. v012=20.18 gms wt..'mr=21.h3 gms
wt. AIBN=0.617S gm: For—0.395
VI-1-3-l 8.0 5.38
VI-l-3-2 214.0 17. 83
71-1-3-3 75.0 25.12

VI-l-3-h 116. O 3 8. 66

 

INSTRUMENTATION
Methods For NMR Spectra

A11 NMR spectra were obtained with a Varian A-60 NMR spectrometer
equipped with a variable temperature probe. The spectra of all the
VClZ-IB copolymers were taken at room temperature in bromobenzene. In
addition to these spectra a series of spectra of sample VI-23-l dissolved
in bromobenzene were obtained at instrument temperature, 64° C, 80° C,
97° C, 1180 C, and 137° C. This sample was also dissolved in tetra—
chloroethylene and an NMR spectrum obtained to study solvent effect.
Although some of the other VClZ-IB samples were originally run at a
higher temperature all data reported for this system will be from the
spectra taken at instrument temperature. The data will be reported for
only the room temperature spectra because of the reduced noise level of
the spectra at this temperature when compared to the spectra taken at
higher temperatures.

With the exception of two samples all the V0124V01 copolymers
were run at room temperature. The two samples which were not run at
room temperature were run at an elevated temperature because the copolymer
precipitated from solution at room temperature.

All chemical shifts were measured using tetramethylsilane (TMS)
as an internal reference and peaks are reported in T values.

The spectra of the VClz-IB system were run once at a 500 cps.
sweep width to obtain the relation of the peaks of the solvent to those
of the copolymer and to optimize the performance of the spectrometer for

the individual samples. To aid in obtaining the areas under the peaks
41

42

the spectra were rerun at a 250 cps. width. All peaks of the copolymer
and that of the reference were visible in this sweep width but the solvent
peaks were not.

Because the signals of the polymer peaks were very weak all spectra
of the VClz-IB. system were run at an amplitude setting of between 8
and 12.5. Other typical settings were: Filter Band Width 0.2;
Radio Frequency Field = 0.06 and a Sweep Time of 500 seconds. Because
of the high spectrum amplitude setting, noise was quite evident in the
spectra which introduced error in the peak area measurements. To
minimize the effect of the noise each spectrum was repeated and super-
imposed three times on the original spectrum; This averaged the noise
somewhat permitting the areas to be traced with greater accuracy.

All spectra of the VCl2-VC1 copolymer were run at a 500 cps.
width. This line width was chosen because these peaks were much broader
than those of the VClz-IB copolymers and they could not have been scanned
at a 250 cps. sweepwidth. The signals from the peaks in these copolymers
were weaker than those in the VClz—IB copolymers and the spectrum ampli-
tude had to be increased. Most of the spectra were taken at an amplitude

setting of 50 or 63. Other settings for the spectra of the VCl -VCl

2
copolymers were: Filter Band Width : 0.1; Radio Frequency Field = 0.2 and
Sweep Time = 500 seconds. I

Since there was considerable noise in the spectra they were
repeated three times superimposing each repeat on the original spectrum

as in the VClz-IB COpolymers. This enabled the areas under the curves

to be measured more accurately.

113'

Method of Measuring Areas Under'Peaks

The areas underneath the peaks in the NMR Spectra were obtained
by first placing the spectra on a light table than tracing the portion
which was to be measured on a piece of white paper. In this manner the
noise could be smoothed and the spectra would not have to be used for
the measurement thus keeping them free from possible damage.

Areas were measured with a planimeter. The planimeter was guided
over the area once then repeated usually with the planimeter in a
different position. If the two areas did not agree by two or three
units the measurements were repeated until good agreement was obtained.
All areas were measured in this manner. (The agreement obtained can be
seen for a typical sample, VI-20-2: Area I readings were 153 and 153;

Area I readings were 253 and 255; Area 2 readings were hhh and hhé.

INTERPRETATION OF NMR.SPECTRA
Assignments of Peaks in'VClz-IB Copolymer Spectra

Figure 3 displays comparative proton.resonance spectra of two
cepolymers of the‘VClz—IB system with different compositions and the
spectra of the two corresponding homopolymers. The spectrum A is of
pure poly(isobutylene), spectrum.B is ofha copolymer with a large amount
of IE in the monomer charge, spectrum C is of a copolymer with approxi—
mately equal amounts of each monomer in the charge, spectrum D is of
pure poly(vinylidene chloride). The spectra of the copolymers are
divided into three main regions labeled X, I, and Z.

In Figure 3 it can be seen by comparison of the two copolymer
spectra with the spectrum of pure poly(vinylidene chloride) that area I
of the copolymers is in the same region as the only peak in the homo-
polymer. This peak in the homopolymer arises from the methylene protons
of the polymer chain. Since these are methylene protons between two
carbons bonded to chlorine the area.X in the copolymer chain is assigned
to the methylene protons of an AA diad where A refers to a vinylidene
chloride unit in the copolymer chain and B refers to an isobutylene
unit in the copolymer chain.

Area Z in the copolymer spectra is in the same region as the
methylene proton and methyl proton peaks of the spectrum of pure poly-
(isobutylene) and is interpreted as arising from the methylene protons
of a.BB died and the methyl protons from all B sequences in the copolymer.

Area'Y in the copolymer spectra is mid-way between areas X and Z.

There are no peaks in this region in the spectra of either of the

hh

 

 

 

 

D
1 1 1 1 4
6 7 8 ”F 9 10

Fig. ‘3. Proton resonance spectra of a homopolymer of isobutylene (A);
a homopolymer of vinylidene chloride (D); a copolymer with mole
fraction 0.48 isobutylene and 0.51 vinylidene chloride (B) s a
copolymer with mole fraction 0.21. isobutylene and 0.76 vinyl-
idene chloride (0).

us
homopolymers. Because this area does lie mid-way between the areas of
the two homopolymers it was deduced that this area arises from the
methylene protons of an AB diad.

One major difficulty in the interpretation of the cepolymer spectra
with regard to the various diads was the appearance of more peaks than
were anticipated. Since there is no sound evidence to the contrary, it
is assumed in this interpretation that the copolymerization resulted
only from head-tail addition. This is a reasonable assumption because
of the steric factors involved in both monomers and the polarity of
the vinylidene chloride monomer and the experimental evidence which
indicated head to tail addition only, in a wide variety of similar
systems. Therefore to interpret the spectra it was necessary to consider
sequences longer than diads. Figure u displays the different possible
four unit sequences of the copolymer. All the methylene protons in the
brackets in Figure u (a, b, and c) are part of an AA diad but upon closer
examination it can be seen that each is from a different set of tetrads.
"a" is an AAAA tetrad, b is an AAAB tetrad, and c is a BAAB tetrad where
A = VC12 and B = IB. If the screening effect of the tetrads are signi-
ficant then the peak of the AA group should split into three smaller
peaks arising from the three possible tetrads formed therefrom. The
AAAA tetrad peak can readily be identified since it is the one which
would be present in the pure homopolymer of poly (vinylidene chloride).
It is located at 6.187'. It is well known (2) that substituting a
halide for a methyl group causes the chemical shift of the proton under
investigation to be moved downfield. On this basis a reasonable assign-
ment of the peak at 6.407. is to the AAAB tetrad and the peak at 6.59

to the BAAB tetrad. In Figure 4 (d, e, f, and g) the methylene protons

147
Fig. h

— 3
twelm
m .3...
films 1
llClc
.0 w H.
.HIILlJll
lluCluC
c . H

Humol

-
1|C|fl
C .IH
Hlnw 3
was
PM“.

. 1-cao
C . H
Hln—u 1
lIClC
C . H
Hlmol

d

 

 

.1—
lnICIC
who we...
—|H I 3
wt 3 mad
Cl P
.WWWhn mTfliflC
.n- 3
1-9m will
0 . s IH
Hlnwlnn H n-u l
3 «3810
.HCAw at. H
w . H Hun—0|
Hume:
h
8

IR
1 thc
qu'Clc Inn
.u. .
3 ..3 Tom
.mho we .. _.mH.nw.um
I I I'H 3
H 3 much
.....J'h.v.l.m -
mlnv H HInWIH
I 3
w m .53 .nc
ICIC no.1H
nuulH HIn—V
H'
alu
.1

he
in the brackets represent the four possible tetrads (AABA, ABAB, AABB,
and BAAB) which are possible from.an AB diad. If each tetrad affects
the central methylene protons in a different manner than four peaks
should be present in the area arising from the methylene protons of the
AB diad. Most of the NMR spectra of the VClQ-IB copolymers obtained in
this work show only two peaks in the AB diad region of the spectrum.
However, the copolymers made with a high concentration of IE in the
monomer charge show a spectra in which the AB region does consist of
four peaks. The reason that such a large concentration of IE is needed
in the monomer charge lies in the relative reactivity of the two monomers
as will be discussed in the next section.

Using the same argument presented for the interpretation of the
tetrad peaks in the AA region the tetrads for the AB diads were assigned
as follows: progressing from the furtherest peak downfield toward the
reference standard there is the AABA tetrad (7.161'), the ABAB tetrad
(7.36T), the use tetrad (7.5V), and finally the 1311313 tetrad (7.62T).
The assignment of the peak (7.367") to the ABAB sequences and the peak
(7.5147,) to the AABB sequences is based on the empirical results rather
than on theoretical grounds. To make the reverse assignment would be
illogical as all experimental evidence will later show that it is extremely
difficult to obtain a BB diad in this system and the peak (7.5hT )
appears only when the most favorable conditions exist for AABB tetrads
and BB diads.

In Figure h (h, i, j) the bracketed methylene protons all arise
from BB diads but from different tetrads. The BBBB tetrad should be
shifted upfield toward the TMS resonance and correspond to the methylene
proton peak in the homopolymer of poly(isobutylene). In spectra B and 0

this peak is much larger than would be expected from the reactivity of

1:9

the monomers and the mole fraction of B in the copolymer. It is also
larger than the peak which corresponds to the methyl group of the pure
homopolymer of poly(isobutylene). Therefore it seems evident that there
are other protons in addition to the methylene protons of the BBBB tetrads
giving rise to this peak. It will be shown later that the other protons
influencing this peak are from the methyl group protons of a triad. If
this interpretation is correct two peaks should be found downfield from
this large peak corresponding to the other two tetrads of the BB died.

In spectrum.B in Figure 3 these two predicted peaks are faintly noticeable.
This is the spectrum of the copolymer containing the greatest concen-
tration of IE in the monomer charge. ‘Most of the spectra have the
appearance of spectrum 0 of Figure 3 where these two peaks are not
apparent.

In Figure 5 are depicted three chain segments with a central IB
unit. If the chemical shift of each methyl group was dependent only on
the groups bonded to the adjacent carbons in the chain then all would
have the same chemical shift as each has a methylene hydrogen group on

‘ CH
each side. But if the carbon atomfl to the ~39 group on the chain is
H3

examined and it is assumed that the groups bonded to these carbons affect
the chemical shift of the methyl groups then each of the three methyl
groups depicted in Figure 5 will display a different chemical shift.

The chemical shift of the methyl group in the chain segment shown
in Figure 5 (c) should be the same as the methyl group in pure polya
(isobutylene).l In Figure 3, Spectra B and 6, this chemical shift
corresponds to the peak (8.7147') which is furthest upfield in the two
spectra. By applying the same logic as was previously used for the

methylene group the next peak downfield (8.677') was assigned to the

50
methyl group in Figure h (b) or an ABB triad and the large peak (8.h87’)
was interpreted as the chain segment depicted in Figure 5 (a), an ABA
triad. This assignment correlates with the reactivities of the two

monomers which predict the ABA peak should be the largest.

$01K CH3' 9].
. -$-é=-¢-¢-?-$-
3H 01 H OH H 01
c1 ‘H 11 CH
b I I I I 3 é I 3
'0'1-1'1'I'?'
I
H 01 H 033 H CH3
H CH3 H CH3 H CH3
c l l l I I I
-a=-°-<I-$ ‘f'?’
H 8H3 H H CH3
Fig. 5

In Figure 6 are displayed the spectra of three additional VClz-IB
copolymers which give further evidence to support the interpretations
discussed above. Figure 6 (A) is the spectrum of VI-18-2, Figure 6 (B)
is the spectrum 0f‘VI-l7-2 and Figure 6 (c) is the spectrum of VI-22-2.
From Table VI it is shown that the amount of IE in the monomer charge
increases from the copolymer in Figure 6 (c) to the copolymer in
Figure 6 (A). In all three samples the mole fraction of IE in the monomer
charge is greater than that in Figure 3 (c) but less than that in
Figure 3 (B). The areas underneath the peaks all vary in the manner one
would expect if this interpretation is valid. As the amount of IE in

the copolymer increases area X decreases and the peak X1 is drastically

51

 

 

 

 

 

 

 

L A I J 1

6 7 8 “r 9 10

Fig. 6. Proton resonance spectra of a copolymer with mole fraction 0.39
isobutylene and 0.61 vinylidene chloride (A); a copolymer with
mole fraction 0.33 isobutylene and 0.67 vinylidene chloride (B);

a copolymer with mole fraction 0.24 isobutylene and 0.76 vinyl-
idene chloride (C).

 

52

effected because there are fewer and fewer AAAA tetrad sequences.
Area'! increases but the area under peak‘Il relative to the area under

Y2 becomes smaller due to the fewer A units in the copolymer.

Peak Assignments in~ Vinylidene Chloride-Vinyl

Chloride Copolymer spectra

Figures 7 and 8 are NMR spectra of copolymers of Y612 and VCl.

The spectra are arranged with the amount of V01 in the copolymer increas-
ing from the top of Figure 7 to the bottom of Figure 8. Because of the
introduction of an asymmetric center into the various copolymer sequences
only diads were able to be unambiguousily identified in this system.

The peak furtherest downfield (5.137’) is designated peak 14 and is
assigned to the CX-hydrogens of the Vol in agreement with previous
workers (5, 13-19). The next peak upfield, N, (6.h2T ) corresponds to
that of pure poly( vinylidene chloride) and is due to AA diads. The

peak at 7.70T , R, is the same as the-methylene protons in pure poly
(viml chloride) and is due to BB diads. Theremaining peak, P, at
6.93T is half way between the AA methylene proton peak and the BB
methylene proton peak. Arguing analogously to the VClg-IB copolymer
system this must be due to the methylene protons of an AB died.

Because the AA diad will be free of any stereosequential effects
this would be the logical place to observe splitting due to tetrads if
they are observable. In Figures 7 and 8 all the spectra except spectrum D
in Figure 8 displays two peaks in the AA diad region. In spectrum D the
AA diad region is composed of a large peak with a shoulder on each side.
The peaks in spectra A, B, and c are at 6.307' and 6.1;27’ while those in

spectrum 1!: are at 6.h2T and 6.58T . The two shoulders in spectrum D are

 

 

 

 

 

 

 

 

A
B
N,
A
P
/"\
C
M
/"\
R
A
1 L l l l l l
1+ 5 6 T 7 8 9 10

Fig. 7. Proton resonance spectra of a copolymer with mole fraction 0.17
vinyl chloride and 0.83 vinylidene chloride (A); a copolymer
with mole fraction 0.26 vinyl chloride and 0.74 vinylidene

chloride (B); a copolymr with mole fraction 0.37 vinyl chloride
and 0.63 vinylidene chloride.

 

54

 

 

D
E
PVC
1 l I l 4 L 1
4 5 6 T 7 8 9 10

Fig. 8. Proton resonance spectra of a homopolynmr of vinyl chloride (PVC);
a copolymer with mole fraction 0.51 vinyl chloride and 0.49
vinylidene chloride (D); a copolymer with mole fraction 0.66
vinyl chloride and 0.31. vinylidene chloride (E).

55
at 6. BOT and 6. 58T with the main peak at 6.142T. From these results
it can be concluded that the AA diad region contains three peaks which
are poorly resolved. These peaks would correspond to the three possible
tetrads which arise from an AA diad. Because the resolution of these
peaks is poor it was not possible to measure the area underneath the
individual peaks and calculate the tetrad structures. However, if one
looks qualitatively at the height of the peaks they-increase and decrease
in the manner corresponding to the reactivities of the_two monomers.

A different interpretation of an NHR spectrum of a VC124VCI
copolymer is offered in the paper by chujo and co-workers (38). They
claim only two peaks are in the methylene region assigned to the
AA diads in this work and that these two peaks result from the normal
head to tail polymerized segments of 7312 and an abnormal head to head
polymerization. For proof of their interpretation they compare the
spectrum of one 70124701 copolymer with that of poly-2,3-dichlorobutadiene
(PDGB) and partially chlorinated poly-2,3-dichlorobutadiene (PCPDCB).
Unfortunately although they claim to have synthesized six low conversion
copolymers of varying feed ratios they show no complete spectra and only
one partial spectrum which depicts just the region in question. This
partial spectrum was from a copolymer synthesized from a‘vclz/Vcl feed
ratio of 85/15 which should contain approximately 95 x or more V312. The
copolymer spectrum.peak which they claim corresponds to the peak in the
m spectrum of man falls 0.15 T further downfield than the PCPDCB peak
which is very poor correlation. The data offered by these workers is
poor and sparse leading to a lack of confidence in their interpretation,
‘but their data is freely interpretable according to the assignments

presented in this work.

56'
Normalization of the NMR Spectra
In Figure 3 the areas labeled X and Y arise from the resonance
of only the methylene protons of the VClz-IB system, whereas the area
labeled 2 is the result of both methylene proton resonance and methyl
proton resonance. Since the areas under the curves are proportional to
the number of protons in a given configuration the normalization is
achieved in the following way:
I = C [ number of AA diads (methylene only)] = Cx(AA)
I = c [ 2 x number of AB diads (metlvlene only)] = crane)
2:: c [ number of BB diads (methylene only)-+ number of AB diads
(methyl only) + number of BB diadsv(methyl ohm]

‘Uhere A = Vc12 unit, B ==IB unit, and c = constant of proportionality.
In an IB unit there are three times as many methyl protons as methylene
protons, thus: .

z = c [h x number of BB diads (methylene equivalents) + 3 x number of

AB diads (methylene equivalents)]

Since I is proportional to 2A3, by subtracting 3;! from Z and dividing
the result by four one obtains a direct proportion to the number of BB
diads, i.e. the number of BB diads is proportional to (lzI - 218).
The mole (or number) fraction of each diad is given by the following

equations where the symbols AA etc. represent the number of each species;

 

 

AA'+ AB +'BA +-BB AA +‘2AB-+-BB

 

AA+ 2AB-+ BB

57

AA+ 2AB+ BB

 

Since all possible diads are defined‘the sum must equal one.
By applying the relationships between the diads and the NHR

areas the following equations for the mole fraction of the diads are

 

 

 

 

obtained:
r“; x z X (5.10
2 BY SI 2
X+Y+E '8— X+E—+’E
X +-E£4+ E
8 14
L2:
SI 2
+-__ ._
x 8 +h

From this derivation it is also possible to determine the mole

fraction of monomer units since,

IA: fAA+fAB and (5.7)

fB = fBA+fBB (5.8)

Only five of the ten possible tetrads are large enough to be
measurable by NHR, but the mole fraction of these tetrads can still be
calculated because the tetrad signals all arise from the methylene protons
and the normalization constant of these protons is the same as C; the
proportionality constant for the diads. Therefore the mole fractions of the

various tetrads are obtained by dividing the area of the tetrad peak by the

factor {+3.33% Labelling the peaks in atypical copolymer spectrum in the X

58
region from left to right as X1,X2, and X3 and the peaks in the Y region from

left to right as Y1 and Y2 the following results are obtained for the tetrads:

f _ 1
AAAA - __ (5.9)
D
x
2f g 2
AAAB __ (5.10)
D
f - X3
BAAB ‘ —— (5.11)
D
2f = Y1
AABA —— (5.12)
D
Y
2fABAB = 2
-— (5.13)
D

WhereD=X+_Sl+_Z_
8 u
The analysis of the VClz-V01 system spectra is more straightforward
than that of the VCl2-IB system. In the copolymer Spectra in Figures 7
and 8 there are four main areas all arising from separate groups of

protons. From the interpretation discussed previously the following

relationships were obtained:

M = C [number of B units in polymer ( a ~hydrogens)] = Cx(B)
N = C [number of AA diads (methylene only)] = Cx(AA)

P = c [2 x number of AB diads (methylene only)] = Cx(2AB)

R = C I number of BB diads (methylene only)] = Cx(BB)

where A = VCl2 unit, B = VCl unit, and C = constant of proportionality.
Equations (5.1), (5.2), and (5.3) are the equations for the mole
(or number) fractions of the various diads and by substituting the above

relations into these equations one obtains:

59

 

 

 

ryA,= N (5.1h)
N +-P“+-R
a”: P Gum
N+P+R .
r R -
m-
N+P+R 5‘“

The mole fraction of viqfl. chloride in the polymer is obtained
from the spectrum by multiplying the area of the (X-hydrogen peak by
two and dividing this number by the total area of the methylene protons,
i.e.,

f3 =, 2M

N-+ P +-R

 

(5.17)

This procedure constitutes an independent check of the mole fractions
in the copolymer and should correspond to the values obtained through
(5.7) and (5.8).

Internal consistency indicates valid assignments of the spectra.

'RESULTS AND DISCUSSION
Results for VClz-IB Copolymer System

From'Price's matrix formulation (50) it is possible to derive
equations for the mole fraction of the various diads in terms of the
ratio of the monomer concentrations in the charge, Fg, and the reactivity
ratios, r1 and r2, (where 1 refers to 7012 and 2 refers to IE) assuming
that only the terminal unit affects the addition of the next monomer
unit and constant monomer feed. The equations (shown below) are the
same as those derived previously by Hall (hS) but are in the nomenclature

of Kinsinger and Colton (S7).

 

 

fAA = rlFo2 (6.1)
r113.0 + 21#0 + 1'2
rlFo + 2Fo+ r2

fBB = ’2 (6.3)

 

Each of these equations can be rearranged in linear form so that
values for r1 and r2 can be easily obtained(58). In the VGlz-IB system only
the first two equations areused because-they correspond with the more

accurate experimental measurements. ‘Rearranging equation (6.1) one

obtains;

61

2 -
2Fo = P0 (1 fAA) z~l - r2 (6.u)

 

fAA

F 2 1 - f ‘
° ( AA __. a straight line with a slope of
f

r1 and an intercept of -r2 18 obtained. Rearranging equation (6.2)

By plotting 2Fo vs.

 

one obtains:
2Fo(l - 2fAB) 2
— 2f = F0 rl+r2 (6.5)
AB
and by plotting the left hand side of (6.5) vs. F02 a slope of r1 and
an intercept of r2 are obtained.

The monomer reactivity ratios can also be calculated from mole
fractions of monomers in the copolymer by applying the Ross-Fineman (#8)
equation (2.1“) which is also restricted to the low conversion terminal
effect mechanism.

Table IX lists the mole fractions of the various diads, the
monomer charges, and the mole fraction of VC12 in the copolymer as
determined by NMR, and the more common standard, carbon analysis and
chlorine analysis. In addition to these results the experimental
tetrad values are listed in Table X.

Plots of these methods for obtaining r1 and r2 from the died and
monomer mole fraction data for the terminal mechanism are displayed
in Figures 9, 10, ll,and 12. Figure 9 represents the fAA diad data;
Figure 10 shows the 2fAB data plotted according to (6.5); Figure 11
displays a Ross-Fineman (#8) plot of the mole fraction data of the
monomers in the polymer from NMR and the carbon analysis of the
copolymers; Figure 12 is another Ross-Fineman plot for the mole fractions

obtained from chlorine analysis of the copolymers.

 

 

62

 

an.0 4o.0 mH.0 No.0 «No.0 Hom.0 aam.0 000.0 m-aH-Hs
0H.0 oo.0 m~.0 0o.0 50m. a0m.0 0a0.0 HNH.0 H-4m-He
0H.0 oo.0 4~.0 oo.0 00m.0 a»m.0 4a0.0 oma.0 H-aN-He
oo.0 No.0 mm.0 am.0 m0m.0 00m.0 0a0.0 00H.0 w-oH-Hs
o0.0 mo. am.0 no.0 mwo.0 «no.0 H4o.0 mmm.0 N-on-He
oo.0 4o.0 «0.0 4o.0 00m.0 mmo.0 m0o.0 0aH.0 H-om-Hs
40.0 no.0 mm.0 4o.0 moo.0 Hoo.0 4a~.0 o0~.0 m-mN-He
40.0 No.0 4m.0 oo.0 0ao.0 o0o.0 ~05.0 ma~.0 H-mN-He
40.0 0o.0 o0.0 oo.0 Hmo.0 Hoo.0 maa.0 mm~.0 m-0m-He
40.0 0o.0 00.0 No.0 amo.0 Hoo.0 mma.0 a4~.0 N-aH-He
40.0 4m.0 «4.0 05.0 oao.0 «ma.0 uH~.0 00N.0 m-oN-Hs
40.0 No.0 44.0 as.0 Hmo.0 mme.0 moo.0 ~H0.0 H-mw-H>
40.0 No.0 m4.0 Ha.0 o0a.0 0HF.0 «oo.0 0H0.0 H-om-He
40.0 04.0 04.0 m~.0 --- --- a4o.0 mmm.o w-om-H>
00.0 o4.0 Hm.0 4a.0 ama.0 am~.0 m0o.0 .Ha0.0 m-om-He
00.0 m4.0 oo.0 oa.0 Nm~.0 ao~.0 mom.0. om4.0 m-wm-Hs
«0.0 0m.0 mm.0 ma.0 moa.0 4m~.0 0mm.0 Ha4.0 H-NH-He
no.0 om.o Ho.o 0o.0 om~.0 m4o.0 mm4.o mom.0 w-4m-Hp
no.0 a~.0 0o.0 no.0 --- --- oa4.0 40m.0 N-Nm-He
m2: .8 cognac

emu meow 3 «Hope: «Hose: «8wa Es. NEE: e380

moods no mmoaaomnm oaoz. .NH edema

 

 

 

Table X. Mole fraction of tetrads

Sample fAAAA fAAAB fBAAB fAABA fABAB
v1-32—2 0.1-1 0.22 0.01- 0.23 0.06
VI-2h-2 0.32 0.21- 0.05 0.31 0.06
VI-12-1 0.28 0.26 0.05 0.31 0.07
VI-22-2 0.23 0.25 0.05 0.33 0.10
VI-28-2 0.21 0.2). 0.06 0.37 0.10
v1-30-2 0.18 0.23 0.06 0.38 0.10
VI-20-l 0.17 0.22 0.06 0.39 0.12
vx-23-1 0.17 0.22 0.07 0.38 0.13
VI-26-2 0.11 0.22 0.09 0.38 0.15
v1-17-2 0.08 0.18 0.11 0.38 0.18
VI-20-2 0.07 0.18 0.11 0.38 0.21
v1-25-1 0.06 0.17 0.12 0.38 0.21
VI-25-2 0.05 0.16 0.12 0.38 0.22
VI-26-1 0.01- 0.15 0.12 0.36 0.21-
VI-18-2 0.03 0.13 0.13 0.31- 0.28
v1-16-2 0.02 0.11 0.12 0.29 0.35
v1-29-1 0.02 0.11 0.12 0.29 0.35
VI-Bh-l 0.01 0.09 0.12 0.27 0.36
VI-l9-2 0.01 0.07 0.11 0.27 0.37

 

o 0030 «a .8 nonsense
32. Hi.“ been: mn-§H\FA§e-Smea u am 0220332 one .8 0.30 365m .0 are

Omw

0.0 04 0.4” 4..” m...“ 0..” 0.0 0.0 4.0 «.0 0.

 

 

 

_ _ _ _ l _ l _ . .

see;
0

 

. O
Aim-H o

No.

 

 

 

 

 

 

 

65

noose me e0 neaoeuno

oHoa u 040 once: Nu+H$Mm u m<MN\AmdmmlavohN gunmmowpsflmn one no uoaa usomfiq .0H .wfim

0.4” m.

o.

0
NM

#0

m. . 0.

 

_ _

_

O.

 

 

 

66

.hpfinmdo you
confine 3H0 N no no 300 Bahamas consume anemones.“ As “memo mxz anemones." ADV
«noahHomoo one. 5 9308020 no 0.3mm oHoa u m use coo.“ one. 5. mnoaoooa no o3?“ oHoa
u oh omen: my I H\%m4..n u M>Hluvoh .mwsmmodpsnou emaomHMImmom on» no pod“ .3213 .3. .03
M

 

NO N.m HO o.

 

 

. _ 4 _ _ _ _ 1 c 0.

NO

 

 

2 - ten

*0

 

 

 

 

 

67

 

 

 

 

 

I I I I I I I
.28——-
.2I-_ ' .4
.20_ __
C)
.16——— . .___
F
fl (f-ll
.12..— _,
O
.th. . _
O
(a . .__
(5)
O
0))

0 0 I I I I I L I

0 0 o 1 0 2 0 3 0.I- 0 5 0 6 0 7

F02
T

Fig. 12. Same coordinates as Fig. 11. Experimental data is from
chlorine analysis of the copolymer.

68

The results for P1 and r2 from these plots are listed in Table XI.

The r2 values obtained from the experimental data are small and in some
cases have negative values, however, this is not an unusual occurrence
‘when small values of r1 or r2 (less than 0.1) are determined by normal
copolymer analysis. For such cases the "r" value is usually listed as

zero but a least squares analysis of the data in the present work show
the negative value for r2 to be significant. With an average value of
r1 = 3.3 and r2 chosen to be 0.05 a plot of the mole fractions of the

three diads vs. the mole fraction of VCl2 in the monomer charge was

 

constructed and is depicted in Figure 13. The correlation between the
theoretical curves using these values for rl and r2 and the experimental
values is good, however, some deviation is noted particularly at low
concentration of VCl2 in the monomer charge. Small changes consistent
with the scatter in the results for r1 and r2 did not improve the fit
with experimental data.

Since the experimental tetrad values were available for the first
time the method for calculating the mole fractions of the tetrads had
to be derived.

The equations for calculating the mole fractions of the various
tetrads for a terminal mechanism can be calculated as outlined from the
theory in Chapter 2 by multiplying the mole fractions of the appropriate
diad by the corresponding conditional probabilities for obtaining the
desired tetrad, e.g.

f

AAAA=f

2 .
AA x PAA x PAA = fAA x (FAA) (6.6)
Since only five of the tetrads were large enough to be measured experi-

mentally equations were derived for these five and are listed below:

69

Table XI Copolymerization reactivity ratios from various data for

vinylidene chloride (1) - isobutylene (2) system

 

 

 

 

 

Method r1 0? r2 0?
1. Carbon analysis
Ross-Fineman Plot 3.210 0.155 -0.007 0.009
2. Chlorine analysis
Ross-Fineman Plot 2.520 0.082 -0.030 0.007
30 fv011frm NHR
Ross-Fineman Plot 2.999 0.057 0.000 0.001
1:. *fAA from NMR
2Fovs F020- " fAA)
f 3.062 0.081 -0.098 0.01b
AA
F0 (1 " fM) .1; 3.11:5 ----- -0.079 -----
fAA F0
6. ZfAB from NMR
V8 Fo 3.h70 0.020 0.088 0.006
2:13

”I- and 5 represent only two different ways of plotting the same data.

I = STANDARD DEVIATION

 

70

 

 

 

 

 

 

 

 

 

1'0 I I I I I I I I I
.8 41—1313 AA“.
r—u—
Cl 610 ‘— 2A8
'6 I quD
D
MFDIADS _ '3 —
El
0
04 '- O
" O
.2 “'7
%A
.0 I I I AA A! i=1=l l
00 .2 04 06 08

MFA

Fig. 13. Hole fraction of diads versus mole fraction of vinylidene
chloride in monomer feed; (0) f ; (0) 2f ; (A) fBB' Solid
lines terminal mechanism r1 = 3990, r2 = .05,

71

NAME = 2rAB x (PM)? (6.8)
fBAAB =fAB x PM x PAB (6.9)
afw :2 2f” X PEA I PM (6.10)

Substituting the various expressions for the probabilities in the case

of the terminal mechanism as derived from‘Pricets paper one obtains:

 

 

 

 

rm, = r“ x ’1F0 (6.12)
r1F0-+
r F 2
mm = 21‘“, x 1 0 (6.13)
rlFo + 1
f — 2!“ X ' rlFo \X/ 1 \ (601(4)
BAAB :
2 r1F0+ 1] \rlFo + 1.;
r2 + F0 rlFo + 1 '

ZfABAB = ZfAB x

 

__F_L_ , ____1__ (6.16)
r2 + F0 r1F0+ 1

The calculated values for the tetrads employing the above equations
with the same r values as used previously were plotted against the mole
fraction of V612 in the charge and compared with the experimental values.
Figures lb and 15 depict these plots. The agreement between the experi-
mental and calculated values is reasonable in Figure 1h but these three

tetrads are less dependent on small changes in r values than are the two

72

u N“ H some _dq.fiaoflw _ H- Av Mmcac — _ e a

«gas nos
0G9-
na 00
«sense
eneoamann
>
No
noHvosAH oHoa
0.9an
mousse
e no mo
“scene
mac:
0 3H 0 NH
.e

0.
m.
I a.
I .m.
We
H.
I o.

 

 

 

 

 

 

 

mnmhpoe

73

 

 

 

 

~° I I I I
05 I_'
.L .— O
O 0 0
[j 001) O
O
.3 ._ O
o 8) U
Tetrads 2W
D
.— CEI
CI
Cl
0 2mm
U
,. I I I I I
at.) 1 o2 3 cl:- 05
FA0
Fig. 15. Same coordinates as 11;: «”2me (A)2fABAB° Solid lines

terminal mechanism r1 : 3.30; r2 = 0.05

(7‘

71-
tetrads plotted in Figure 15 where correlation between the experimental

and calculated values is poor. Since the r values used were averages of
several values other r values within reason were tried but there was no
improvement in correlation between the experimental and calculated
values for the tetrads.

The small divergence between calculated and experimental diads
and the larger divergence of the tetrads is the trend predicted by Berger
and Kuntz (51) in their paper on the distinction between terminal and
penultimate mechanisms when the assumed copolymerization mechanism is
not the correct one. They point out the need to know the distribution
of more than Just the monomers and diads in the copolymer in order to
distinguish between the two mechanisms. Before the present work no
accurate work was presented which permitted the determination of the
mole fraction of sequences of higher order than diads.

Based on this evidence the assumption that the terminal mechanism
is the correct mechanism for this copolymer system does not appear a
valid assumption.

Since the terminal mechanism appears invalid another mechanism must
be offered to explain the microstructure of this copolymer system. The
second simplest copolymerization mechanism is the penultimate unit
mechanism and this mechanism was tested next.

‘When the penultimate unit mechanism is assumed the equations for
the diads become more complex since additional parameters are introduced.
The equations for the mole fractions of the various diads for the
‘penultimate mechanism were derived from.the procedure outlined in'Price's

‘paper (50). The results are listed below:

75

 

 

 

fAA .,—_ __ (X (6.17)
0( +20 + 7
21‘“; = 2,0 (6:13)
CX-t 2y3-ejr
fBB 7 (6.19)
f Ct + Efl + 7
Where C1 ____ rl'Fo2

 

rl'Foz + 11132170 + F0 + 1'2

2?

2,0= °

rlFoz + rlrzFo + F0 4" r2

 

r2'

 

7:

rl‘Fo2 4’ r’11‘2'Fo 4‘ I"o + 1'2 '

k k k k
andr1=fl, rl'-_-:._B_M;, r2=_B£,andr2'=.4A-B—B- .
kAAB AB kBBA lflUflk

Note that the penultimate case requires four independent parameters whereas
the diads give Just two independent pieces of data. Because these equa-
tions for the mole fraction of the diads are of a quadratic form in F0, no
linear plot could be derived to determine the various r values. However,
by deriving the equations for the mole fractions of the five measureable
tetrads and applying simple algebra it was possible to determine the
various r values.

The equations for the tetrad mole fractions are derived in a manner

similar to those of the terminal case and are listed below:

f 1‘1F 2
Am :— I'M x 0 (6.20)
rlFo + l

76

 

 

 

 

 

 

 

 

2me :: 2113 x I rlFO \ 3‘ rl'FO (6.21)
\ rlFo + 1 I r1 'F0 4" 1
r 'F' \ 1
me ,____ fAB x 1 O x (6.22)
rl'FO +- 1 I l + rlFo
2fAABA :ZfAB x 11.1?" \ x F° (6.23)
rl'Fo+1l Fo’f‘rZ'
1
ZfABAB : ZfAB 3: F0 X( (602(4)
Fo+r2' 1+'rl'Fo

The ratio of fAAAB/fBAAB gives rlFo (59 ). By plotting this ratio
versus F0, r1 is obtained from the slope. In a similar manner the ratio
of fAABA/IABAB gives rl'Fo and from the slope of a similar plot rl' is
obtained. The parameter r2! can be obtained through the ratio (R) of
{AB/:AABA‘ A linear plot of (R - 1)F’o2 versus Fo gives an independent
value for rl' and r2'. Finally r2 is obtained by substituting the other
parameters into a diad formula and calculating r2 for the series of Fb's.
An average r2 over the complete set of data was then calculated. Figures
16 through 18 depict these various plots. The values obtained from these
ratios and plots were: r1 = 2.95, r1' = 6.22, r2 = 0.15, and r2' = 0.02.

These values were employed to calculate the various diads and tetrads.
The calculated and experimental died and tetrad values versus HFVCIQ are
displayed in Figures 19, 20, and 21. The agreement between the experimental
and calculated values is excellent in all three figures.

Figure 15 shows that the experimental values for the ABAB sequences

were lower than those calculated using the reactivity ratio values derived

from the terminal mechanism. A possible explanation for this discrepancy

77

.smammnooe opmaapasmom no ,
M an masses 00330 .0m meI-mb <4
4... a... 0 PH mam o o m . .
am.“ \ a 3m oH was

 

m¢<¢w

o. O
m m H 04 m.0 0.0

 

0.0

 

«.0

11.0

,0.0

 

,m.0

 

 

 

78

\

0.:

m.m

0.m

m.~

mend
402.“
0.0

 

m;

0.4..

m.0

0.0

 

 

 

 

 

1

 

1

 

 

 

 

 

0.0

«.0

4.0

0.0

0.0

00H

79

.oHnmmoHesHon mama Eonm bondsnopos ma summonses

opmsdpassom one now .mu Ho osamp one .00 msmnm> womflalmm<¢M\m<Hv Ho moan smegma 4 .ma .mah
<3“.

HI.
0.1..

men

 

0.0

3.0

N.0

0.0

 

 

 

 

_

0CD

_

C) (D

 

0.0

III «~00

 

 

a...“

 

 

 

 

 

 

 

 

 

 

.7
I | I I I
e?
O O '0 AA
0
.6‘-— e . D .—
e
I
D -—I
e
e
. ._
e
QAB
A
IA A I‘ :0
ch 05 06 CI,
“A

Fig. 19. Same coordinates as Fig. 13; (EDfM; (0)2f B; (A)f . Solid lines
penultimate mechanism r1 = 2.95; r1! = 6.22; r2 = 8715; r2! = 0.02.

81

 

 

 

 

.6
I I I I
.5 ~— —
A
cal-I I” —
Te‘t reds AAAA
A
. t“- -—
A
U
“ I
2AAAB I
__‘.
e . 0
I
.5 . o

 

Fig. 20. Same coordinates as 11:: (A)f ; ((3)2f ; (0)1‘BAAB.
Solid lines penultimate mechan sm r1 -..= 2.9 ; r1! = 6.22;
1'27: 00020; E=O-'5

 

.II

Tetrads

.3

.2

.1

82

 

 

 

 

penultimate mechanism r1 = 2.9 ; r1' = 6.22; r2 = 0.15;

1‘2 ' = 09020

7‘
030 O 0 O o
. 2AABA
O ‘\
O
I
I
II
I
' 21113113
I
" D
I
I I
.2 .3 .I.I
”FA
Fig. 21. Same coordinates as 11.: (0)2f A3 (CDHABAB: Solid lines

 

83
is shown by the reactivity ratios calculated seeming the penultimate
mechanism. The values of r2 and r2' are close to the r2 values of the
terminal mechanism and the r1 value is close to the r1 value of the
teminal mechanism. However, the rl' value is almost twice as large as

k
r1. The value rl' is a ratio of BAA and since this value is greater
1:
BAB
than r1 it seems to indicate that placing an IB unit next to a terminal

701 unit enhances the addition of another 7012 unit to a greater degree

 

2

than placing a 7012 next to a terminal 7012. This would result in fewer

BABA sequences than predicted by the terminal mechanism.

In Smary
The study has presented a new set of linear equations for the mole

 

 

fraction of diads in terms of monomer feed ratios. From these equations

values for r and r can be determined from died sequences which are

l 2
independent of the mole fraction of mere in the chain.

The choice of vinylidene chloride and isobutylene as monomers
for the copolymarization was based strictly on the favorable symmetrical
geometry and the simplicity of the proton enviroments in the monomers and
homopolymers. The chemical shifts of the methylene proton resonances ‘in
the two homopolymers were sufficiently spread to lead to a well defined
and resolvable series of peaks in the copolymer spectrum. Although a
total analysis of the spectrum was not completed the assignments and
subsequent calculations of the r1 and r2 values as determined from the
chemical analysis and the diad NMR analysis correspond and are ample
evidence that these assignments are correct. Further proof of the validity
of these assigmnents can be found in a recent publication by Hellwege and
co-workers (60) who independently studied this copolyimr system and are
in complete agreement with the interpretation presented in this
work. Innumerable earlier attempts to assign these peaks and
normalize the data resulted in a complete breakdown

8h
or disagreementwith the simple theory.

The results of the NMR study of this copolymer system demonstrate
the validity of the work of Berger and_kuntz. The knowledge of sequences
of higher order obtained by NMR has permitted the terminal mechanism to
be ruled out in this system. The penultimate mechanism has been proposed
as the correct one and seems to explain the data in a satisfactory manner.
However, it should be noted that according to their a values.this monomer
pair is not one which would be predicted to obey such a mechanism.
Alternate mechanisms can be proposed which may also account for the
microstructure and still be consistent with the reactivity of the
monomers. The study of the microstructure of this system is the first

bonafide example of such a study for copolymers.
Results for'VClzéVCl Copolymer System

Table XII lists the mole fraction of V012 in the copolymer by NHR
and chemical analysis, the mole fraction of'V012 in the monomer charge,
and the mole fractions of the various diads.

The diad equations for fAA and ZfAB along with the Ross-Fineman
equation for monomer concentrations were used to calculate r1 and r2
for the terminal mechanism. The graphs for these equations are shown in
Figures 22,-23, 2nd 2h. Figure 25 shows a Ross—Fineman plot using the
two chemical anaLysis (carbon and chlorine) to determine the mole fraction
of monomer in the polymer. The results of the various plots are shown
in Table XIII along with the standard deviation of each method.

Average values of the monomer reactivity ratios excluding chemical
analysis were computed and the results were; r1'= 3.75 and r2::0.18. These

values were employed to construct a plot of the mole fractions of the three

 

 

Table XII.

Vinylidene chloride-vinyl chloride copolymerization

 

 

 

Sample MFvc12 vaclg fAA efls £33 M£V012 M£v012
NMR carbon Cl
Wei-63 -2 0. 691 0. 887 0. 807 0. 183 0.010 ----- -----
vvcl-62-2 0.576 0.832 0.716 0.265 0.019 0.872 0.933
vv01-36-2 0.h70 0.769 0.619 0.320 0.059 0.701 0.751
vv01-67-2 0.395 0.7h3 0.5uh 0.39h 0.062 ..........
vv01-6h-2 0.355 0.72h 0.h93 0.h28 0.079 0.671 0.669
vv01-61-2 0.272 0.627 0.387 0.h96 0.117 0.505 0.58h
vv01-69-2 0.2h0 - 0.603 0.3h3 0.h97 0.160 --.-- -----
vv01-66-2 0.203 0.5h2 0.287 0.512 0.201 0.u23 0.h59
vv01-65-2 0.169 0.h93 0.227 0.521 0.252 ----- -----
vvci-h7-2 0.098 0.3h1 0.121 0.u57 0.h2h 0.331 0.327
vv01-7o-2 0.066 0.266 0.063 0.389 0.5h8 ----------

 

86
Table XIII Copolymerization reactivity ratios from various data for

vinylidene chloride(l)-vinyl chloride (2) system.

 

 

Method r1 61 r2 62

 

1. Carbon
analysis
Ross-Fineman plot 3.36 2.72 .07 .20

2. Chlorine
analysis
Ross-Fineman plot 3.31 1.29 .26 .1h

 

30 fVCl? from
NMR Ross-Fineman

plot 3.30 0.085 .13 .015
h. fAA from NHR
20(1 ' fAA) v3.1, b.02 0.007 .15 .002
3AA F0

5. 2fAB from NMR
210(1 - 2rAB)
ZfAB

vs. sz 3.95 0.0h2 .26 .059

 

6. Literature value 3.2 .30

 

87

 

 

 

 

 

 

 

 

.3 .o .l .8 .9 1.0 1.]

:1-rAA)

 

F0
iii

Fig. 22. Linear plot of the relationship F°(1-fM)/fM -_-. r2/Fo-rl
where f = mole fraction of AA diads.

88

U6

I

L.’

.1 ;

.uefie ma .3 compose.“

39.. u 3e once. ms 1. race 0 maemkmaemuioem managed..." as» no peas .323 .3 .92

0.5

0.6

o.n

m2:

 

Asses; yes...

1...:

o.m.

(\J

0..”

 

 

l

 

 

04

 

 

89

o.«

wé

.3933.» 52 Scam spec Hepeoeauog

0.4

:4

v.

H

Amnev
o;

}

H

oh

m5

.manmmogwaou fiEoflmnmmom 23 Mo no.3 usefiq .3 .mg

0.0 3.0 N.o 0.0 N.on

 

 

_

 

 

N.

m.

D.

.mambaenm 05.3.20 some one on: 30:59:00 use AOV {ashamed
scheme ace.“ one on: p033. was ADVnmEmeogeaou gassedmlmmom on» mo #33 .3053 .mm .mam

 

00.

,mo.

OH.

ma. 3...: mm.

,ON.

mm.

on.

 

 

 

 

mn.

 

91
diads versus the mole fraction of'V012 in the monomer charge. The
experimental diad.mole fractions were included for comparison and the
results displayed in Figure 26. The values obtained from.this analysis
compare favorably with those found in the literature (61).

Because the NHR spectra of the vc124V01 system were not as sharply
defined as were the NHR spectra of the VClz-IB copolymers due in part to
the poorer solubility and in part to the different possible stereosequences
they could not be analyzed for tetrads. Although the terminal mechanism
of copolymerization was assumed in this work and the agreement between
the calculated died values and experimental diad values is good one cannot
discard the possibility of another copolymerization mechanism without

data on longer sequences.
Results of Conversion study

Prior to the discovery that the terminal mechanism does not seem
to be the correct one for the vulg-IB system a study of the effect of
conversion on the various sequences was undertaken. since the theoretical
development has only progressed considering this effect of conversion on
diads and since the terminal mechanism gives moderate correlation with
the experimental diads, the results presented in this work are assumed to
be valid within experimental error for the terminal mechanism. Two series
of conversion runs were made with this system. The results for these
series are listed in Table XIV. Figures 27 and 28 are plots of conversion
versus mole fraction of monomers in the polymer and conversion versus mole
fraction of diads for the series with F0 = 0.9h1. The line represents
the calculated values which were obtained from a computer program of

equations (2.36) and equations in Table'v assuming r1-= 3.3 and r23=.0.05.

92

 

 

40H.0 mme.0 ~00.0 0mm.0 00m.0 a.0m m0~.0 mam.0 ermuaan
0ma.0 000.0 H40.0 0:m.0 ma:.0 H.mm m0~.0 mam.0 mum.H-H>
00~.0 000.0 ~40.0 mmm.0 Hm4.0 0.aa m0~.0 mam.0 «-mrH-H>
Hmmd $0.0 0mo.o mamd m3.o “mm mmmé mend 76...”qu
Nam.0 N-.0 040.0 004.0 004.0 ~.Nm «0.0 0:0.0 «-mnm0.H>
540.0 0wa.0 H;0.0 004.0 004.0 0.0: 00.0 0:m.0 NumnmauHe
0-.0 Hma.0 am0.0 50;.0 0m:.0 N.0m No.0 0:m.0 ~sm-ma.H>
0H0.0 mma.0 0m0.0 040.0 0am.0 p.50 No.0 0:m.0 «-0smean
005.0 0m~.0 0m0.0 m0:.0 00m.0 :.0m «0.0 0:m.0 ~-N-m4.H>
«00.0 0m~.0 0m0.0 ~m:.0 :mm.0 0.aH «0.0 0:m.0 ~a4.ms.H0
saa.0 a0».0 mm0.0 0am.0 Ham.0 0.: «0.0 04a.0 NuanmauHe

e an mm“ menu saw .5060 u «Hosea: mm seesaw

 

 

00.780 soaenobmoo ugoaoo 333033703820 28039.; .5 0.3.2.

93

 

 

 

 

1.0
l I F
M
0.8 __
0.6 "— .—
Diafls O
‘ DEID 0
D
0.11 — D _
D
AB
0.2 _
O
'7 F A BB
M l I i
1.0 0.2 0.11 0.6 0.8 1.0
MFA
Fig. 26.

Hole fraction of diads of VCl-V012 system versus mole fraction
of vixwlidene chloride in monomer mixg' (OHM; ((3)2113;
(A)fBB. solid lines terminal mechanism r1: 3.75 r2 = 0.18.

9h

GOH mu 0b:0 0

m0» 0.0 mom “0: won wow “3 0
_ _ _ _ _ 00.0

 

1:.m0.0

2.0
N
Hoes

BRO

 

 

 

effico

 

9S

.m0.0u N.100 u .E
06.30508 H0550» seamen?” 05A .mmidv Educ“: «S‘fiov 530002.80
9000 000 00000» sepshm neehaoeoo mHano>.ma evade no moap00nm 0Hoa Ho voam .mw .mHm

moaeuepsoo
no . m8 mom m0: . mom mom mom 0.
. f 0 1 LH b O
\! _ a mm a d _ G d
4 < a

 

 

Q <4

 

03.20 mt

 

 

 

 

96
The trends of the experimental diad mole fractions are in thesame
direction as the calculated values indicating the equations are a reason-
able approximation of the actual process.

‘Much more work needs tote done in this particular area but the work
presented here has demonstrated the feasibility of such a study. ‘Hith
the aid of computers the calculations involved in the theoretical aspects
of this problem.will become less tedious and it may be possible to

extend the theory to other copolymerization kinetic mechanisms.
Conclusion

The results of this work have shown NMR to be an acceptable working
tool for the polymer chemist in the determination of the microstructure
of copolymers. There are several advantages and some limitations in the
use of man for microstructure determinations.’

There is more information available on the microstructure through
NHR than has previously been determined with other methods of analysis.
No microstructure units any larger than diads have been reported on
synthetic copolymers by other means. ‘With NHR one does not have to
rely only on chemical analysis to determine reactivity ratios or mole
fractions of the monomer in the copolymer. Because the copolymer needs
only to be dissolved in a solvent to be run in the NMR it is not
destroyed and can.be used for further testing. Another plus factor is
the reproducibility of the results obtained from the NHR data of the
systems studied.

NHR studies of copolymers do. have some limitations. The choice
of monomers is the greatest limitation. The copolymer produced from the

.monomers must be soluble in suitable solvents i.e. solvents which dissolve

97
the copolymer but do not interfere with the copolymer spectra. It is

also desirable for the chemical shift of the methylene protons of the

two homopolymers to be far enough apart to permit the detection of another
peak or group of peaks which will arise from the AB pairs. The two systems
of the present work meet this requirement quite readily especially in the
case of the VClg-IB system where the AB peaks are easily resolvable from
either of the homopolymer peaks. Signals from other protons of the homo-
polymers such as the methyl group protons in 13 must not interfere with
the regions of the methylene proton peaks in such a manner that makes
interpretation of the spectra impossible. In the NHR spectra of the
VClz-IB system there was overlap of the methyl and methylene proton peaks
in the 2 region of the spectra. This overlap was overcome by normaliza-
tion of the peak areas as explained in Chapter V. The (X—hydrogens of

the V01 in the‘VClzJVCl system did not interfere with the rest of the
spectra and were, in fact, an independent check on the mole fractions of
each monomer found in the polymer.

The results of the studies of the two systems shows that the
mathematical treatments of copolymerization which have been proposed by
Price and his predecessors are valid. The results of both systems show
that calculated values and experimental values agree within the limits
of the experiments. The fit of the equations for the mole fraction of
diads is good in both copolymer systems when the penultimate mechanism
was assumed for the first system and the terminal mechanism was assumed
for the second system. In addition to the good agreement for the diads
the experimental and calculated tetrad values were also in good agreement

in the VClZ-IB system when the penultimate mechanism was assumed.

98
The experimental results of the conversion study of the VCiz-IB

system have shown trends in the direction predicted by theory and although
further work needs to be done in this area the work done to date has not

refuted the theoretical assumptions.

7.

8.

9.
lo.

11.

12.

1h.
15.
16.
17.
18.

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APPENDIXI

Solutions For V399 and the copolymer composition Equation for k =- 2

Utilizing F. price to Methods.

1. Solutions PoanQ)
The V3”) arecomponents of a four column vector V”) which
represent the relative concentrations of diads in the various states.

The solutions for V3”) which we want are given by the equation

v3<2) .___ 3,16
where A38 is the cofaetor of the element A38 in the determinant IAI and
c is the constant.

Because the matrix (P) which is an arrangement of transition
probabilities as shown below is stochastic, it can be shown that the
determinant IAI can be formed by subtracting unity from each element

of the diagonal of the matrix (P). Thus:

 

 

r 1
. P00 0 1-P21 0
H» 0 P21 0
(P) : 0°
0 P12 0 1-P33
L 0 1-P12 0 P33 J
and
Poo-1 O 1-P21 0
l-Poo -1 P21 0
H =
0 P12 -1 21.-1’33
0 l-P12 0 P33-l

 

 

1 03

104

and to obtain solutions for the various V 3(2) all we need to do is

obtain the appropriate cofactors. Thus

-1 P21 0

Von) ml 1’12 '1 1"1’33

 

 

1

_ C <( -1)( -1)(P33-1)-P21 [P12(P33-1)’( 1'P33)(1’P12)]>
: C(P33-1)(1'P21)

and

 

l"'l’oo P21 0

V1( 2) z: c 0 -1 1-‘P33

 

0 0 P33 -1

 

=-_ c(1-Poo)(P33-1)

 

and similarly
1400 -1 o
2
v2( )= c 0 P12 1433
o 1412 933-1

 

:: c(1-Poo)(P33-l) 1' V1( 2)

 

Also
l"Poo '1 P21
2 .. ..
V3( )_ c 0 P12 1
0 1-P12 0

 

= 9(1-Poo)(1-P12)

105

2. Solution For Copolymer Composition Equation
Rom equation 2.21
No V0“) + V2(2)

% - g .52). ,3(2)

 

We can then substitute the previously determined values for the VJ(2)'s
and obtain

No ~ (P33-l)(1-P21) + (ls-POOXP33-1)

111 ‘ (14.016334) +(1-2..)<1-212)

which can be written

 

 

 

+ (l-lel

No _ (1'Poo)

”1 (1412)
l +

(1-1’33)

To place this equation in a form utilizing the reactivity ratios and
initial concentrations of the monomers, the definitions and equation 2.22

in chapter two must be used. The definitions usedzrnz :13 when 11

km

rn= in}; when n is odd and E =Fo.
k... n.

is even,

Applying equation 2.22

1"'00 = koono
koomo ‘1' k011‘11

By dividing both top and bottom of the right hand side by kOlnl and

 

applying the definitions we obtain

roro+ 1

 

106

Ski-1”]! 1’12 = kloHo F0

k1o'“o + k11"1 "1 “’ Fo

 

and P21: 1‘21!]. _ 1
R201% + k211‘1 1 "' x'ol'b

 

 

also 933: k31H1 __ 1‘3

 

substituting these expressions in the equation for {9, one obtains:
N1

( 1-___1__)
1 + r2Fo

(1.. .1636...)
”oFo’r 1

1+

 

 

111 F0
(1- _-
I"o + 1.1

(1.. _JL.)
1'3 + F0

)

1+

 

This is the identical equation derived by Alfrey and Goldfinger for the
penultimate mechanism of. copolymerization.

It- I'M—x.“ 4
A

O

, =__

,‘1

 

,.
ml:

"I7'1111111111111111